Results of Jacobian Elliptic Functions
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 22.2#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k = \frac{\Jacobithetaq{2}^{2}@{0}{q}}{\Jacobithetaq{3}^{2}@{0}{q}}} | k = ((JacobiTheta2(0, q))^(2))/((JacobiTheta3(0, q))^(2)) |
k == Divide[(EllipticTheta[2, 0, q])^(2),(EllipticTheta[3, 0, q])^(2)] |
Failure | Failure | Error | Successful [Tested: 3] |
| 22.2#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{\prime} = \frac{\Jacobithetaq{4}^{2}@{0}{q}}{\Jacobithetaq{3}^{2}@{0}{q}}} | sqrt(1 - (k)^(2)) = ((JacobiTheta4(0, q))^(2))/((JacobiTheta3(0, q))^(2)) |
Sqrt[1 - (k)^(2)] == Divide[(EllipticTheta[4, 0, q])^(2),(EllipticTheta[3, 0, q])^(2)] |
Failure | Failure | Error | Successful [Tested: 3] |
| 22.2#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = \frac{\pi}{2}\Jacobithetaq{3}^{2}@{0}{q}} | EllipticK(k) = (Pi)/(2)*(JacobiTheta3(0, q))^(2) |
EllipticK[(k)^2] == Divide[Pi,2]*(EllipticTheta[3, 0, q])^(2) |
Failure | Failure | Error | Failed [1 / 3]
{DirectedInfinity[] <- {Rule[k, 1]} |
| 22.2.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = \frac{\pi z}{2\compellintKk@{k}}} | zeta = (Pi*z)/(2*EllipticK(k)) |
\[Zeta] == Divide[Pi*z,2*EllipticK[(k)^2]] |
Failure | Failure | Error | Failed [210 / 210]
{Complex[0.8660254037844387, 0.49999999999999994] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.7059984047169785, -0.6365247818792681] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.2.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{z}{k} = \frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}}} | JacobiSN(z, k) = (JacobiTheta3(0, q))/(JacobiTheta2(0, q))*(JacobiTheta1(zeta, q))/(JacobiTheta4(zeta, q)) |
JacobiSN[z, (k)^2] == Divide[EllipticTheta[3, 0, q],EllipticTheta[2, 0, q]]*Divide[EllipticTheta[1, \[Zeta], q],EllipticTheta[4, \[Zeta], q]] |
Failure | Failure | Error | Failed [140 / 210]
{Complex[0.1017958925630662, 9.78035129055685*^-4] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.08293092681074243, -0.5359189266558633] <- {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.2.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}} = \frac{1}{\Jacobiellnsk@{z}{k}}} | (JacobiTheta3(0, q))/(JacobiTheta2(0, q))*(JacobiTheta1(zeta, q))/(JacobiTheta4(zeta, q)) = (1)/(JacobiNS(z, k)) |
Divide[EllipticTheta[3, 0, q],EllipticTheta[2, 0, q]]*Divide[EllipticTheta[1, \[Zeta], q],EllipticTheta[4, \[Zeta], q]] == Divide[1,JacobiNS[z, (k)^2]] |
Failure | Failure | Error | Failed [140 / 210]
{Complex[-0.1017958925630662, -9.780351290556814*^-4] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.08293092681074243, 0.5359189266558634] <- {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{z}{k} = \frac{\Jacobithetaq{4}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{2}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}}} | JacobiCN(z, k) = (JacobiTheta4(0, q))/(JacobiTheta2(0, q))*(JacobiTheta2(zeta, q))/(JacobiTheta4(zeta, q)) |
JacobiCN[z, (k)^2] == Divide[EllipticTheta[4, 0, q],EllipticTheta[2, 0, q]]*Divide[EllipticTheta[2, \[Zeta], q],EllipticTheta[4, \[Zeta], q]] |
Failure | Failure | Error | Failed [140 / 210]
{Complex[-0.08257811120249814, 0.0027270134984790223] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.13231049687767538, 0.2777560839806882] <- {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.2.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{4}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{2}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}} = \frac{1}{\Jacobiellnck@{z}{k}}} | (JacobiTheta4(0, q))/(JacobiTheta2(0, q))*(JacobiTheta2(zeta, q))/(JacobiTheta4(zeta, q)) = (1)/(JacobiNC(z, k)) |
Divide[EllipticTheta[4, 0, q],EllipticTheta[2, 0, q]]*Divide[EllipticTheta[2, \[Zeta], q],EllipticTheta[4, \[Zeta], q]] == Divide[1,JacobiNC[z, (k)^2]] |
Failure | Failure | Error | Failed [140 / 210]
{Complex[0.08257811120249814, -0.002727013498479031] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.13231049687767538, -0.2777560839806882] <- {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{z}{k} = \frac{\Jacobithetaq{4}@{0}{q}}{\Jacobithetaq{3}@{0}{q}}\frac{\Jacobithetaq{3}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}}} | JacobiDN(z, k) = (JacobiTheta4(0, q))/(JacobiTheta3(0, q))*(JacobiTheta3(zeta, q))/(JacobiTheta4(zeta, q)) |
JacobiDN[z, (k)^2] == Divide[EllipticTheta[4, 0, q],EllipticTheta[3, 0, q]]*Divide[EllipticTheta[3, \[Zeta], q],EllipticTheta[4, \[Zeta], q]] |
Failure | Failure | Error | Failed [140 / 210]
{Complex[-0.11217526698173597, -1.5044574583405517] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-1.6119897435833945, -2.3508894631681736] <- {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{4}@{0}{q}}{\Jacobithetaq{3}@{0}{q}}\frac{\Jacobithetaq{3}@{\zeta}{q}}{\Jacobithetaq{4}@{\zeta}{q}} = \frac{1}{\Jacobiellndk@{z}{k}}} | (JacobiTheta4(0, q))/(JacobiTheta3(0, q))*(JacobiTheta3(zeta, q))/(JacobiTheta4(zeta, q)) = (1)/(JacobiND(z, k)) |
Divide[EllipticTheta[4, 0, q],EllipticTheta[3, 0, q]]*Divide[EllipticTheta[3, \[Zeta], q],EllipticTheta[4, \[Zeta], q]] == Divide[1,JacobiND[z, (k)^2]] |
Failure | Failure | Error | Failed [140 / 210]
{Complex[0.112175266981736, 1.5044574583405517] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.6119897435833943, 2.350889463168173] <- {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsdk@{z}{k} = \frac{\Jacobithetaq{3}^{2}@{0}{q}}{\Jacobithetaq{2}@{0}{q}\Jacobithetaq{4}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{3}@{\zeta}{q}}} | JacobiSD(z, k) = ((JacobiTheta3(0, q))^(2))/(JacobiTheta2(0, q)*JacobiTheta4(0, q))*(JacobiTheta1(zeta, q))/(JacobiTheta3(zeta, q)) |
JacobiSD[z, (k)^2] == Divide[(EllipticTheta[3, 0, q])^(2),EllipticTheta[2, 0, q]*EllipticTheta[4, 0, q]]*Divide[EllipticTheta[1, \[Zeta], q],EllipticTheta[3, \[Zeta], q]] |
Failure | Failure | Error | Failed [138 / 210]
{Complex[-0.10264566281694597, 1.7190366283522571] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.005017214212665183, 0.8218706074973681] <- {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{3}^{2}@{0}{q}}{\Jacobithetaq{2}@{0}{q}\Jacobithetaq{4}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{3}@{\zeta}{q}} = \frac{1}{\Jacobielldsk@{z}{k}}} | ((JacobiTheta3(0, q))^(2))/(JacobiTheta2(0, q)*JacobiTheta4(0, q))*(JacobiTheta1(zeta, q))/(JacobiTheta3(zeta, q)) = (1)/(JacobiDS(z, k)) |
Divide[(EllipticTheta[3, 0, q])^(2),EllipticTheta[2, 0, q]*EllipticTheta[4, 0, q]]*Divide[EllipticTheta[1, \[Zeta], q],EllipticTheta[3, \[Zeta], q]] == Divide[1,JacobiDS[z, (k)^2]] |
Failure | Failure | Error | Failed [138 / 210]
{Complex[0.1026456628169461, -1.7190366283522573] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.005017214212665148, -0.8218706074973681] <- {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcdk@{z}{k} = \frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{2}@{\zeta}{q}}{\Jacobithetaq{3}@{\zeta}{q}}} | JacobiCD(z, k) = (JacobiTheta3(0, q))/(JacobiTheta2(0, q))*(JacobiTheta2(zeta, q))/(JacobiTheta3(zeta, q)) |
JacobiCD[z, (k)^2] == Divide[EllipticTheta[3, 0, q],EllipticTheta[2, 0, q]]*Divide[EllipticTheta[2, \[Zeta], q],EllipticTheta[3, \[Zeta], q]] |
Failure | Failure | Error | Failed [140 / 210]
{Complex[-0.23207264303523145, 2.174081147069575] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.3131092646447684, 1.178043032175558] <- {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{2}@{0}{q}}\frac{\Jacobithetaq{2}@{\zeta}{q}}{\Jacobithetaq{3}@{\zeta}{q}} = \frac{1}{\Jacobielldck@{z}{k}}} | (JacobiTheta3(0, q))/(JacobiTheta2(0, q))*(JacobiTheta2(zeta, q))/(JacobiTheta3(zeta, q)) = (1)/(JacobiDC(z, k)) |
Divide[EllipticTheta[3, 0, q],EllipticTheta[2, 0, q]]*Divide[EllipticTheta[2, \[Zeta], q],EllipticTheta[3, \[Zeta], q]] == Divide[1,JacobiDC[z, (k)^2]] |
Failure | Failure | Error | Failed [140 / 210]
{Complex[0.23207264303523142, -2.174081147069575] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.3131092646447683, -1.178043032175558] <- {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.2.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsck@{z}{k} = \frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{4}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{2}@{\zeta}{q}}} | JacobiSC(z, k) = (JacobiTheta3(0, q))/(JacobiTheta4(0, q))*(JacobiTheta1(zeta, q))/(JacobiTheta2(zeta, q)) |
JacobiSC[z, (k)^2] == Divide[EllipticTheta[3, 0, q],EllipticTheta[4, 0, q]]*Divide[EllipticTheta[1, \[Zeta], q],EllipticTheta[2, \[Zeta], q]] |
Failure | Failure | Error | Failed [140 / 210]
{Complex[0.2180891710993932, -0.009050644683206828] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.13880139985550538, -0.6261898650931494] <- {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.2.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{3}@{0}{q}}{\Jacobithetaq{4}@{0}{q}}\frac{\Jacobithetaq{1}@{\zeta}{q}}{\Jacobithetaq{2}@{\zeta}{q}} = \frac{1}{\Jacobiellcsk@{z}{k}}} | (JacobiTheta3(0, q))/(JacobiTheta4(0, q))*(JacobiTheta1(zeta, q))/(JacobiTheta2(zeta, q)) = (1)/(JacobiCS(z, k)) |
Divide[EllipticTheta[3, 0, q],EllipticTheta[4, 0, q]]*Divide[EllipticTheta[1, \[Zeta], q],EllipticTheta[2, \[Zeta], q]] == Divide[1,JacobiCS[z, (k)^2]] |
Failure | Failure | Error | Failed [140 / 210]
{Complex[-0.2180891710993933, 0.009050644683206842] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.13880139985550533, 0.6261898650931494] <- {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.2.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genJacobiellk{p}{q}@{z}{k} = \ifrac{\Jacobithetatau{p}@{z}{\tau}}{\Jacobithetatau{q}@{z}{\tau}}} | genJacobiellk(p)*q* z*k = (JacobiThetap(z,exp(I*Pi*tau)))/(JacobiThetaq(z,exp(I*Pi*tau))) |
genJacobiellk(p)*q* z*k == Divide[EllipticTheta[p, z, Exp[I*Pi*(\[Tau])]],EllipticTheta[q, z, Exp[I*Pi*(\[Tau])]]] |
Failure | Failure | Error | Failed [300 / 300] {Plus[Times[Complex[0.5000000000000001, 0.8660254037844386], genJacobiellk], Times[Complex[-0.31964140165035193, 0.682988488811487], EllipticTheta[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.1897367196265697, 0.08493465422971205]]]] <- {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Times[Complex[0.26976733074627424, -0.3419272748333145], genJacobiellk], Times[-1.0, EllipticTheta[Power[E, Times[Complex[0, Rational[1, 6]], Pi]], Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.1897367196265697, 0.08493465422971205]], Power[EllipticTheta[Power[E, Times[-1, Pi, EllipticK[-3], Power[EllipticK[4], -1]]], Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.1897367196265697, 0.08493465422971205]], -1]]] <- {Rule[k, 2], Rule[p, Power[E, Times[Co
|
| 22.2.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau = \ifrac{\iunit\ccompellintKk@{k}}{\compellintKk@{k}}} | tau = (I*EllipticCK(k))/(EllipticK(k)) |
\[Tau] == Divide[I*EllipticK[1-(k)^2],EllipticK[(k)^2]] |
Failure | Failure | Error | Failed [30 / 30]
{Complex[0.8660254037844387, 0.49999999999999994] <- {Rule[k, 1], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.4867361401447923, 0.0147898206680519] <- {Rule[k, 2], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk^{2}@{z}{k}+\Jacobiellcnk^{2}@{z}{k} = k^{2}\Jacobiellsnk^{2}@{z}{k}+\Jacobielldnk^{2}@{z}{k}} | (JacobiSN(z, k))^(2)+ (JacobiCN(z, k))^(2) = (k)^(2)* (JacobiSN(z, k))^(2)+ (JacobiDN(z, k))^(2) |
(JacobiSN[z, (k)^2])^(2)+ (JacobiCN[z, (k)^2])^(2) == (k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (JacobiDN[z, (k)^2])^(2) |
Successful | Successful | - | Successful [Tested: 21] |
| 22.6.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2}\Jacobiellsnk^{2}@{z}{k}+\Jacobielldnk^{2}@{z}{k} = 1} | (k)^(2)* (JacobiSN(z, k))^(2)+ (JacobiDN(z, k))^(2) = 1 |
(k)^(2)* (JacobiSN[z, (k)^2])^(2)+ (JacobiDN[z, (k)^2])^(2) == 1 |
Successful | Successful | - | Successful [Tested: 21] |
| 22.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1+\Jacobiellcsk^{2}@{z}{k} = k^{2}+\Jacobielldsk^{2}@{z}{k}} | 1 + (JacobiCS(z, k))^(2) = (k)^(2)+ (JacobiDS(z, k))^(2) |
1 + (JacobiCS[z, (k)^2])^(2) == (k)^(2)+ (JacobiDS[z, (k)^2])^(2) |
Successful | Successful | - | Successful [Tested: 21] |
| 22.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2}+\Jacobielldsk^{2}@{z}{k} = \Jacobiellnsk^{2}@{z}{k}} | (k)^(2)+ (JacobiDS(z, k))^(2) = (JacobiNS(z, k))^(2) |
(k)^(2)+ (JacobiDS[z, (k)^2])^(2) == (JacobiNS[z, (k)^2])^(2) |
Successful | Successful | - | Successful [Tested: 21] |
| 22.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}+1 = \Jacobielldck^{2}@{z}{k}} | 1 - (k)^(2)*(JacobiSC(z, k))^(2)+ 1 = (JacobiDC(z, k))^(2) |
1 - (k)^(2)*(JacobiSC[z, (k)^2])^(2)+ 1 == (JacobiDC[z, (k)^2])^(2) |
Failure | Failure | Failed [21 / 21] 21/21]: [[.7126235439-1.151829144*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}.144618294+.733840068e-1*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[0.7126235442208428, -1.1518291435850532] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.14461829395996295, 0.07338400615035004] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldck^{2}@{z}{k} = {k^{\prime}}^{2}\Jacobiellnck^{2}@{z}{k}+k^{2}} | (JacobiDC(z, k))^(2) = 1 - (k)^(2)*(JacobiNC(z, k))^(2)+ (k)^(2) |
(JacobiDC[z, (k)^2])^(2) == 1 - (k)^(2)*(JacobiNC[z, (k)^2])^(2)+ (k)^(2) |
Failure | Failure | Failed [21 / 21] 21/21]: [[.287376456+1.151829144*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}.855381706-.733840068e-1*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{1.0 <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.4338548818798933, 0.22015201845104385] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k} = k^{2}(\Jacobiellcdk^{2}@{z}{k}-1)} | - (k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(2) = (k)^(2)*((JacobiCD(z, k))^(2)- 1) |
- (k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(2) == (k)^(2)*((JacobiCD[z, (k)^2])^(2)- 1) |
Failure | Failure | Failed [21 / 21] 21/21]: [[-1.287376456-1.151829144*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}4.672736560+.4694177821*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[-1.2873764557791572, -1.1518291435850532] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[4.672736560761239, 0.46941777772332965] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2}(\Jacobiellcdk^{2}@{z}{k}-1) = {k^{\prime}}^{2}(1-\Jacobiellndk^{2}@{z}{k})} | (k)^(2)*((JacobiCD(z, k))^(2)- 1) = 1 - (k)^(2)*(1 - (JacobiND(z, k))^(2)) |
(k)^(2)*((JacobiCD[z, (k)^2])^(2)- 1) == 1 - (k)^(2)*(1 - (JacobiND[z, (k)^2])^(2)) |
Failure | Failure | Failed [21 / 21] 21/21]: [[-1.287376456-1.151829144*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}1.168184140+.1173544454*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[-1.2873764557791576, -1.1518291435850534] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.1681841401903128, 0.11735444443083248] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{2z}{k} = \frac{2\Jacobiellsnk@{z}{k}\Jacobiellcnk@{z}{k}\Jacobielldnk@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}} | JacobiSN(2*z, k) = (2*JacobiSN(z, k)*JacobiCN(z, k)*JacobiDN(z, k))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) |
JacobiSN[2*z, (k)^2] == Divide[2*JacobiSN[z, (k)^2]*JacobiCN[z, (k)^2]*JacobiDN[z, (k)^2],1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] |
Failure | Aborted | Successful [Tested: 21] | Successful [Tested: 21] |
| 22.6.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{2z}{k} = \frac{\Jacobiellcnk^{2}@{z}{k}-\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}} | JacobiCN(2*z, k) = ((JacobiCN(z, k))^(2)- (JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) |
JacobiCN[2*z, (k)^2] == Divide[(JacobiCN[z, (k)^2])^(2)- (JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] |
Failure | Aborted | Successful [Tested: 21] | Successful [Tested: 21] |
| 22.6.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobiellcnk^{2}@{z}{k}-\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}} = \frac{\Jacobiellcnk^{4}@{z}{k}-{k^{\prime}}^{2}\Jacobiellsnk^{4}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}} | ((JacobiCN(z, k))^(2)- (JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) = ((JacobiCN(z, k))^(4)-1 - (k)^(2)*(JacobiSN(z, k))^(4))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) |
Divide[(JacobiCN[z, (k)^2])^(2)- (JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] == Divide[(JacobiCN[z, (k)^2])^(4)-1 - (k)^(2)*(JacobiSN[z, (k)^2])^(4),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] |
Failure | Failure | Failed [21 / 21] 21/21]: [[.8884947272+1.003906290*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}12.71128264-7.657522619*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[0.88849472735544, 1.0039062900432163] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[12.711282681655987, -7.657522555241993] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{2z}{k} = \frac{\Jacobielldnk^{2}@{z}{k}-k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}} | JacobiDN(2*z, k) = ((JacobiDN(z, k))^(2)- (k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) |
JacobiDN[2*z, (k)^2] == Divide[(JacobiDN[z, (k)^2])^(2)- (k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] |
Failure | Aborted | Successful [Tested: 21] | Successful [Tested: 21] |
| 22.6.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobielldnk^{2}@{z}{k}-k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}} = \frac{\Jacobielldnk^{4}@{z}{k}+k^{2}{k^{\prime}}^{2}\Jacobiellsnk^{4}@{z}{k}}{1-k^{2}\Jacobiellsnk^{4}@{z}{k}}} | ((JacobiDN(z, k))^(2)- (k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) = ((JacobiDN(z, k))^(4)+ (k)^(2)*1 - (k)^(2)*(JacobiSN(z, k))^(4))/(1 - (k)^(2)* (JacobiSN(z, k))^(4)) |
Divide[(JacobiDN[z, (k)^2])^(2)- (k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] == Divide[(JacobiDN[z, (k)^2])^(4)+ (k)^(2)*1 - (k)^(2)*(JacobiSN[z, (k)^2])^(4),1 - (k)^(2)* (JacobiSN[z, (k)^2])^(4)] |
Failure | Failure | Failed [21 / 21] 21/21]: [[-1.000000000+0.*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}-29.55188938+16.70732208*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[-1.0000000000000002, -1.1102230246251565*^-16] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-29.55188948724943, 16.70732193870979] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcdk@{2z}{k} = \frac{\Jacobiellcdk^{2}@{z}{k}-{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k}\Jacobiellndk^{2}@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}} | JacobiCD(2*z, k) = ((JacobiCD(z, k))^(2)-1 - (k)^(2)*(JacobiSD(z, k))^(2)* (JacobiND(z, k))^(2))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(4)) |
JacobiCD[2*z, (k)^2] == Divide[(JacobiCD[z, (k)^2])^(2)-1 - (k)^(2)*(JacobiSD[z, (k)^2])^(2)* (JacobiND[z, (k)^2])^(2),1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(4)] |
Failure | Aborted | Failed [21 / 21] 21/21]: [[.6073373021+.4789879505*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}.5744703200+.1556450229*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[0.6073373022896961, 0.47898795042922426] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.5744703197186243, 0.15564502146829437] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsdk@{2z}{k} = \frac{2\Jacobiellsdk@{z}{k}\Jacobiellcdk@{z}{k}\Jacobiellndk@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}} | JacobiSD(2*z, k) = (2*JacobiSD(z, k)*JacobiCD(z, k)*JacobiND(z, k))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(4)) |
JacobiSD[2*z, (k)^2] == Divide[2*JacobiSD[z, (k)^2]*JacobiCD[z, (k)^2]*JacobiND[z, (k)^2],1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(4)] |
Failure | Aborted | Failed [21 / 21] 21/21]: [[1.189544202+1.637439170*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}-.5756484648e-1+.8251147581*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[1.189544200468709, 1.6374391687321102] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.05756484595277844, 0.825114758131751] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellndk@{2z}{k} = \frac{\Jacobiellndk^{2}@{z}{k}+k^{2}\Jacobiellsdk^{2}@{z}{k}\Jacobiellcdk^{2}@{z}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{4}@{z}{k}}} | JacobiND(2*z, k) = ((JacobiND(z, k))^(2)+ (k)^(2)* (JacobiSD(z, k))^(2)* (JacobiCD(z, k))^(2))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(4)) |
JacobiND[2*z, (k)^2] == Divide[(JacobiND[z, (k)^2])^(2)+ (k)^(2)* (JacobiSD[z, (k)^2])^(2)* (JacobiCD[z, (k)^2])^(2),1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(4)] |
Failure | Aborted | Failed [21 / 21] 21/21]: [[1.247856974+1.526848242*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}-.1237018962-.8644962079e-1*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[1.2478569728519586, 1.5268482411210251] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.1237018961558749, -0.0864496199922923] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldck@{2z}{k} = \frac{\Jacobielldck^{2}@{z}{k}+{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}\Jacobiellnck^{2}@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}} | JacobiDC(2*z, k) = ((JacobiDC(z, k))^(2)+1 - (k)^(2)*(JacobiSC(z, k))^(2)* (JacobiNC(z, k))^(2))/(1 -1 - (k)^(2)*(JacobiSC(z, k))^(4)) |
JacobiDC[2*z, (k)^2] == Divide[(JacobiDC[z, (k)^2])^(2)+1 - (k)^(2)*(JacobiSC[z, (k)^2])^(2)* (JacobiNC[z, (k)^2])^(2),1 -1 - (k)^(2)*(JacobiSC[z, (k)^2])^(4)] |
Failure | Aborted | Failed [21 / 21] 21/21]: [[-1.456738398+.1506627644*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}-4.350355103-.3722352376e-1*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[-1.456738400104645, 0.15066276425673586] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-4.350355102633989, -0.03722352327899177] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellnck@{2z}{k} = \frac{\Jacobiellnck^{2}@{z}{k}+\Jacobiellsck^{2}@{z}{k}\Jacobielldck^{2}@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}} | JacobiNC(2*z, k) = ((JacobiNC(z, k))^(2)+ (JacobiSC(z, k))^(2)* (JacobiDC(z, k))^(2))/(1 -1 - (k)^(2)*(JacobiSC(z, k))^(4)) |
JacobiNC[2*z, (k)^2] == Divide[(JacobiNC[z, (k)^2])^(2)+ (JacobiSC[z, (k)^2])^(2)* (JacobiDC[z, (k)^2])^(2),1 -1 - (k)^(2)*(JacobiSC[z, (k)^2])^(4)] |
Failure | Aborted | Failed [21 / 21] 21/21]: [[1.356171111+.335718656*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}.3210452605+.1984107752*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[1.356171110076661, 0.3357186535359711] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.3210452604978905, 0.19841077324251138] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsck@{2z}{k} = \frac{2\Jacobiellsck@{z}{k}\Jacobielldck@{z}{k}\Jacobiellnck@{z}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{4}@{z}{k}}} | JacobiSC(2*z, k) = (2*JacobiSC(z, k)*JacobiDC(z, k)*JacobiNC(z, k))/(1 -1 - (k)^(2)*(JacobiSC(z, k))^(4)) |
JacobiSC[2*z, (k)^2] == Divide[2*JacobiSC[z, (k)^2]*JacobiDC[z, (k)^2]*JacobiNC[z, (k)^2],1 -1 - (k)^(2)*(JacobiSC[z, (k)^2])^(4)] |
Failure | Aborted | Failed [21 / 21] 21/21]: [[1.370082581+.423198902*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}.2742031773e-1-2.068263955*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[1.3700825790735573, 0.42319889849983916] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.027420317388659004, -2.068263954207401] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellnsk@{2z}{k} = \frac{\Jacobiellnsk^{4}@{z}{k}-k^{2}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}} | JacobiNS(2*z, k) = ((JacobiNS(z, k))^(4)- (k)^(2))/(2*JacobiCS(z, k)*JacobiDS(z, k)*JacobiNS(z, k)) |
JacobiNS[2*z, (k)^2] == Divide[(JacobiNS[z, (k)^2])^(4)- (k)^(2),2*JacobiCS[z, (k)^2]*JacobiDS[z, (k)^2]*JacobiNS[z, (k)^2]] |
Failure | Aborted | Successful [Tested: 21] | Successful [Tested: 21] |
| 22.6.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldsk@{2z}{k} = \frac{k^{2}{k^{\prime}}^{2}+\Jacobielldsk^{4}@{z}{k}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}} | JacobiDS(2*z, k) = ((k)^(2)*1 - (k)^(2)+ (JacobiDS(z, k))^(4))/(2*JacobiCS(z, k)*JacobiDS(z, k)*JacobiNS(z, k)) |
JacobiDS[2*z, (k)^2] == Divide[(k)^(2)*1 - (k)^(2)+ (JacobiDS[z, (k)^2])^(4),2*JacobiCS[z, (k)^2]*JacobiDS[z, (k)^2]*JacobiNS[z, (k)^2]] |
Failure | Aborted | Failed [14 / 21] 14/21]: [[-.1079800431-2.783083843*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2}-6.118875072+.736498896*I <- {z = 1/2*3^(1/2)+1/2*I, k = 3} |
Failed [14 / 21]
{Complex[-0.10798004208618706, -2.7830838428160787] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-6.118875073385709, 0.7364988890066191] <- {Rule[k, 3], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcsk@{2z}{k} = \frac{\Jacobiellcsk^{4}@{z}{k}-{k^{\prime}}^{2}}{2\Jacobiellcsk@{z}{k}\Jacobielldsk@{z}{k}\Jacobiellnsk@{z}{k}}} | JacobiCS(2*z, k) = ((JacobiCS(z, k))^(4)-1 - (k)^(2))/(2*JacobiCS(z, k)*JacobiDS(z, k)*JacobiNS(z, k)) |
JacobiCS[2*z, (k)^2] == Divide[(JacobiCS[z, (k)^2])^(4)-1 - (k)^(2),2*JacobiCS[z, (k)^2]*JacobiDS[z, (k)^2]*JacobiNS[z, (k)^2]] |
Failure | Aborted | Failed [21 / 21] 21/21]: [[-.528217681e-1+.9827060369*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}.7198669539e-1+1.855389227*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[-0.05282176850410922, 0.9827060372847245] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.07198669472412605, 1.8553892285440545] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1-\Jacobiellcnk@{2z}{k}}{1+\Jacobiellcnk@{2z}{k}} = \frac{\Jacobiellsnk^{2}@{z}{k}\Jacobielldnk^{2}@{z}{k}}{\Jacobiellcnk^{2}@{z}{k}}} | (1 - JacobiCN(2*z, k))/(1 + JacobiCN(2*z, k)) = ((JacobiSN(z, k))^(2)* (JacobiDN(z, k))^(2))/((JacobiCN(z, k))^(2)) |
Divide[1 - JacobiCN[2*z, (k)^2],1 + JacobiCN[2*z, (k)^2]] == Divide[(JacobiSN[z, (k)^2])^(2)* (JacobiDN[z, (k)^2])^(2),(JacobiCN[z, (k)^2])^(2)] |
Failure | Aborted | Successful [Tested: 21] | Successful [Tested: 21] |
| 22.6.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1-\Jacobielldnk@{2z}{k}}{1+\Jacobielldnk@{2z}{k}} = \frac{k^{2}\Jacobiellsnk^{2}@{z}{k}\Jacobiellcnk^{2}@{z}{k}}{\Jacobielldnk^{2}@{z}{k}}} | (1 - JacobiDN(2*z, k))/(1 + JacobiDN(2*z, k)) = ((k)^(2)* (JacobiSN(z, k))^(2)* (JacobiCN(z, k))^(2))/((JacobiDN(z, k))^(2)) |
Divide[1 - JacobiDN[2*z, (k)^2],1 + JacobiDN[2*z, (k)^2]] == Divide[(k)^(2)* (JacobiSN[z, (k)^2])^(2)* (JacobiCN[z, (k)^2])^(2),(JacobiDN[z, (k)^2])^(2)] |
Failure | Aborted | Successful [Tested: 21] | Successful [Tested: 21] |
| 22.6.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk^{2}@{\tfrac{1}{2}z}{k} = \frac{1-\Jacobiellcnk@{z}{k}}{1+\Jacobielldnk@{z}{k}}} | (JacobiSN((1)/(2)*z, k))^(2) = (1 - JacobiCN(z, k))/(1 + JacobiDN(z, k)) |
(JacobiSN[Divide[1,2]*z, (k)^2])^(2) == Divide[1 - JacobiCN[z, (k)^2],1 + JacobiDN[z, (k)^2]] |
Failure | Aborted | Successful [Tested: 21] | Successful [Tested: 21] |
| 22.6.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1-\Jacobiellcnk@{z}{k}}{1+\Jacobielldnk@{z}{k}} = \frac{1-\Jacobielldnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})}} | (1 - JacobiCN(z, k))/(1 + JacobiDN(z, k)) = (1 - JacobiDN(z, k))/((k)^(2)*(1 + JacobiCN(z, k))) |
Divide[1 - JacobiCN[z, (k)^2],1 + JacobiDN[z, (k)^2]] == Divide[1 - JacobiDN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 21] |
| 22.6.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1-\Jacobielldnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})} = \frac{\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}-{k^{\prime}}^{2}}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})}} | (1 - JacobiDN(z, k))/((k)^(2)*(1 + JacobiCN(z, k))) = (JacobiDN(z, k)- (k)^(2)* JacobiCN(z, k)-1 - (k)^(2))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k))) |
Divide[1 - JacobiDN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])] == Divide[JacobiDN[z, (k)^2]- (k)^(2)* JacobiCN[z, (k)^2]-1 - (k)^(2),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])] |
Failure | Failure | Failed [21 / 21] 21/21]: [[Float(infinity)+.1810063706*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}-1.050510101+1.261106800*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{DirectedInfinity[] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-1.0505101013872702, 1.2611068009765694] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk^{2}@{\tfrac{1}{2}z}{k} = \frac{-{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}+k^{2}\Jacobiellcnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})}} | (JacobiCN((1)/(2)*z, k))^(2) = (-1 - (k)^(2)+ JacobiDN(z, k)+ (k)^(2)* JacobiCN(z, k))/((k)^(2)*(1 + JacobiCN(z, k))) |
(JacobiCN[Divide[1,2]*z, (k)^2])^(2) == Divide[-1 - (k)^(2)+ JacobiDN[z, (k)^2]+ (k)^(2)* JacobiCN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])] |
Failure | Aborted | Failed [21 / 21] 21/21]: [[1.140351911+.1810063706*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}1.153509822-.96502865e-2*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[1.140351911309134, 0.18100637055769858] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.1535098215093709, -0.009650286433913441] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{-{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}+k^{2}\Jacobiellcnk@{z}{k}}{k^{2}(1+\Jacobiellcnk@{z}{k})} = \frac{{k^{\prime}}^{2}(1-\Jacobielldnk@{z}{k})}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})}} | (-1 - (k)^(2)+ JacobiDN(z, k)+ (k)^(2)* JacobiCN(z, k))/((k)^(2)*(1 + JacobiCN(z, k))) = (1 - (k)^(2)*(1 - JacobiDN(z, k)))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k))) |
Divide[-1 - (k)^(2)+ JacobiDN[z, (k)^2]+ (k)^(2)* JacobiCN[z, (k)^2],(k)^(2)*(1 + JacobiCN[z, (k)^2])] == Divide[1 - (k)^(2)*(1 - JacobiDN[z, (k)^2]),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])] |
Failure | Failure | Failed [21 / 21] 21/21]: [[Float(infinity)+Float(infinity)*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}-1.304876195-.1041070951*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{DirectedInfinity[] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-1.304876194963382, -0.10410709518022829] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{{k^{\prime}}^{2}(1-\Jacobielldnk@{z}{k})}{k^{2}(\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k})} = \frac{{k^{\prime}}^{2}(1+\Jacobiellcnk@{z}{k})}{{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}}} | (1 - (k)^(2)*(1 - JacobiDN(z, k)))/((k)^(2)*(JacobiDN(z, k)- JacobiCN(z, k))) = (1 - (k)^(2)*(1 + JacobiCN(z, k)))/(1 - (k)^(2)+ JacobiDN(z, k)- (k)^(2)* JacobiCN(z, k)) |
Divide[1 - (k)^(2)*(1 - JacobiDN[z, (k)^2]),(k)^(2)*(JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2])] == Divide[1 - (k)^(2)*(1 + JacobiCN[z, (k)^2]),1 - (k)^(2)+ JacobiDN[z, (k)^2]- (k)^(2)* JacobiCN[z, (k)^2]] |
Failure | Failure | Failed [21 / 21] 21/21]: [[Float(infinity)-Float(infinity)*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}.315116621e-1+.1309658139*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Indeterminate <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.03151166205333389, 0.13096581390504758] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk^{2}@{\tfrac{1}{2}z}{k} = \frac{k^{2}\Jacobiellcnk@{z}{k}+\Jacobielldnk@{z}{k}+{k^{\prime}}^{2}}{1+\Jacobielldnk@{z}{k}}} | (JacobiDN((1)/(2)*z, k))^(2) = ((k)^(2)* JacobiCN(z, k)+ JacobiDN(z, k)+1 - (k)^(2))/(1 + JacobiDN(z, k)) |
(JacobiDN[Divide[1,2]*z, (k)^2])^(2) == Divide[(k)^(2)* JacobiCN[z, (k)^2]+ JacobiDN[z, (k)^2]+1 - (k)^(2),1 + JacobiDN[z, (k)^2]] |
Failure | Aborted | Successful [Tested: 21] | Successful [Tested: 21] |
| 22.6.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{k^{2}\Jacobiellcnk@{z}{k}+\Jacobielldnk@{z}{k}+{k^{\prime}}^{2}}{1+\Jacobielldnk@{z}{k}} = \frac{{k^{\prime}}^{2}(1-\Jacobiellcnk@{z}{k})}{\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k}}} | ((k)^(2)* JacobiCN(z, k)+ JacobiDN(z, k)+1 - (k)^(2))/(1 + JacobiDN(z, k)) = (1 - (k)^(2)*(1 - JacobiCN(z, k)))/(JacobiDN(z, k)- JacobiCN(z, k)) |
Divide[(k)^(2)* JacobiCN[z, (k)^2]+ JacobiDN[z, (k)^2]+1 - (k)^(2),1 + JacobiDN[z, (k)^2]] == Divide[1 - (k)^(2)*(1 - JacobiCN[z, (k)^2]),JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2]] |
Failure | Failure | Failed [21 / 21] 21/21]: [[Float(infinity)+Float(infinity)*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}.3945345066-.4550295262*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{DirectedInfinity[] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.39453450618395575, -0.455029526456568] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{{k^{\prime}}^{2}(1-\Jacobiellcnk@{z}{k})}{\Jacobielldnk@{z}{k}-\Jacobiellcnk@{z}{k}} = \frac{{k^{\prime}}^{2}(1+\Jacobielldnk@{z}{k})}{{k^{\prime}}^{2}+\Jacobielldnk@{z}{k}-k^{2}\Jacobiellcnk@{z}{k}}} | (1 - (k)^(2)*(1 - JacobiCN(z, k)))/(JacobiDN(z, k)- JacobiCN(z, k)) = (1 - (k)^(2)*(1 + JacobiDN(z, k)))/(1 - (k)^(2)+ JacobiDN(z, k)- (k)^(2)* JacobiCN(z, k)) |
Divide[1 - (k)^(2)*(1 - JacobiCN[z, (k)^2]),JacobiDN[z, (k)^2]- JacobiCN[z, (k)^2]] == Divide[1 - (k)^(2)*(1 + JacobiDN[z, (k)^2]),1 - (k)^(2)+ JacobiDN[z, (k)^2]- (k)^(2)* JacobiCN[z, (k)^2]] |
Failure | Failure | Failed [21 / 21] 21/21]: [[Float(infinity)-Float(infinity)*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}-.3624296261+.6038808640*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Indeterminate <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.3624296259668921, 0.6038808642712606] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genJacobiellk{p}{q}^{2}@{\tfrac{1}{2}z}{k} = \frac{\genJacobiellk{p}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}{\genJacobiellk{q}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}} | genJacobiellk(p)*(q)^(2)* (1)/(2)*zk = (genJacobiellk(p)*s* z*k + genJacobiellk(r)*s* z*k)/(genJacobiellk(q)*s* z*k + genJacobiellk(r)*s* z*k) |
genJacobiellk(p)*(q)^(2)* Divide[1,2]*zk == Divide[genJacobiellk(p)*s* z*k + genJacobiellk(r)*s* z*k,genJacobiellk(q)*s* z*k + genJacobiellk(r)*s* z*k] |
Failure | Failure | Error | Failed [300 / 300]
{Plus[Complex[-0.9999999999999999, -2.7755575615628914*^-17], Times[Complex[0.0, 0.5], genJacobiellk, zk]] <- {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[s, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-0.9999999999999999, -2.7755575615628914*^-17], Times[Complex[0.0, 0.5], genJacobiellk, zk]] <- {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[s, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\genJacobiellk{p}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}}{\genJacobiellk{q}{s}@{z}{k}+\genJacobiellk{r}{s}@{z}{k}} = \frac{\genJacobiellk{p}{q}@{z}{k}+\genJacobiellk{r}{q}@{z}{k}}{1+\genJacobiellk{r}{q}@{z}{k}}} | (genJacobiellk(p)*s* z*k + genJacobiellk(r)*s* z*k)/(genJacobiellk(q)*s* z*k + genJacobiellk(r)*s* z*k) = (genJacobiellk(p)*q* z*k + genJacobiellk(r)*q* z*k)/(1 + genJacobiellk(r)*q* z*k) |
Divide[genJacobiellk(p)*s* z*k + genJacobiellk(r)*s* z*k,genJacobiellk(q)*s* z*k + genJacobiellk(r)*s* z*k] == Divide[genJacobiellk(p)*q* z*k + genJacobiellk(r)*q* z*k,1 + genJacobiellk(r)*q* z*k] |
Failure | Failure | Error | Failed [300 / 300]
{Plus[Complex[0.9999999999999999, 2.7755575615628914*^-17], Times[Complex[0.7500000000000001, 0.2990381056766578], Power[Plus[1.0, Times[Complex[-0.7500000000000001, -1.2990381056766578], genJacobiellk]], -1], genJacobiellk]] <- {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[s, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.9999999999999999, 2.7755575615628914*^-17], Times[Complex[1.5000000000000002, 0.5980762113533156], Power[Plus[1.0, Times[Complex[-1.5000000000000002, -2.5980762113533156], genJacobiellk]], -1], genJacobiellk]] <- {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[s, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.6.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\genJacobiellk{p}{q}@{z}{k}+\genJacobiellk{r}{q}@{z}{k}}{1+\genJacobiellk{r}{q}@{z}{k}} = \frac{\genJacobiellk{p}{r}@{z}{k}+1}{\genJacobiellk{q}{r}@{z}{k}+1}} | (genJacobiellk(p)*q* z*k + genJacobiellk(r)*q* z*k)/(1 + genJacobiellk(r)*q* z*k) = (genJacobiellk(p)*r* z*k + 1)/(genJacobiellk(q)*r* z*k + 1) |
Divide[genJacobiellk(p)*q* z*k + genJacobiellk(r)*q* z*k,1 + genJacobiellk(r)*q* z*k] == Divide[genJacobiellk(p)*r* z*k + 1,genJacobiellk(q)*r* z*k + 1] |
Failure | Failure | Error | Failed [300 / 300]
{Plus[-1.0, Times[Complex[-0.7500000000000001, -0.2990381056766578], Power[Plus[1.0, Times[Complex[-0.7500000000000001, -1.2990381056766578], genJacobiellk]], -1], genJacobiellk]] <- {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[-1.0, Times[Complex[-1.5000000000000002, -0.5980762113533156], Power[Plus[1.0, Times[Complex[-1.5000000000000002, -2.5980762113533156], genJacobiellk]], -1], genJacobiellk]] <- {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[r, -1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.7.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{z}{k} = \frac{(1+k_{1})\Jacobiellsnk@{z/(1+k_{1})}{k_{1}}}{1+k_{1}\Jacobiellsnk^{2}@{z/(1+k_{1})}{k_{1}}}} | JacobiSN(z, k) = ((1 + k[1])* JacobiSN(z/(1 + k[1]), k[1]))/(1 + k[1]*(JacobiSN(z/(1 + k[1]), k[1]))^(2)) |
JacobiSN[z, (k)^2] == Divide[(1 + Subscript[k, 1])* JacobiSN[z/(1 + Subscript[k, 1]), (Subscript[k, 1])^2],1 + Subscript[k, 1]*(JacobiSN[z/(1 + Subscript[k, 1]), (Subscript[k, 1])^2])^(2)] |
Failure | Aborted | Successful [Tested: 21] | Successful [Tested: 21] |
| 22.7.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{z}{k} = \frac{\Jacobiellcnk@{z/(1+k_{1})}{k_{1}}\Jacobielldnk@{z/(1+k_{1})}{k_{1}}}{1+k_{1}\Jacobiellsnk^{2}@{z/(1+k_{1})}{k_{1}}}} | JacobiCN(z, k) = (JacobiCN(z/(1 + k[1]), k[1])*JacobiDN(z/(1 + k[1]), k[1]))/(1 + k[1]*(JacobiSN(z/(1 + k[1]), k[1]))^(2)) |
JacobiCN[z, (k)^2] == Divide[JacobiCN[z/(1 + Subscript[k, 1]), (Subscript[k, 1])^2]*JacobiDN[z/(1 + Subscript[k, 1]), (Subscript[k, 1])^2],1 + Subscript[k, 1]*(JacobiSN[z/(1 + Subscript[k, 1]), (Subscript[k, 1])^2])^(2)] |
Failure | Aborted | Successful [Tested: 21] | Successful [Tested: 21] |
| 22.7.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{z}{k} = \frac{\Jacobielldnk^{2}@{z/(1+k_{1})}{k_{1}}-(1-k_{1})}{1+k_{1}-\Jacobielldnk^{2}@{z/(1+k_{1})}{k_{1}}}} | JacobiDN(z, k) = ((JacobiDN(z/(1 + k[1]), k[1]))^(2)-(1 - k[1]))/(1 + k[1]- (JacobiDN(z/(1 + k[1]), k[1]))^(2)) |
JacobiDN[z, (k)^2] == Divide[(JacobiDN[z/(1 + Subscript[k, 1]), (Subscript[k, 1])^2])^(2)-(1 - Subscript[k, 1]),1 + Subscript[k, 1]- (JacobiDN[z/(1 + Subscript[k, 1]), (Subscript[k, 1])^2])^(2)] |
Failure | Aborted | Successful [Tested: 21] | Successful [Tested: 21] |
| 22.8.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@@{(u+v)}{k} = \frac{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{v}{k}+\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{u}{k}}{1-k^{2}\Jacobiellsnk^{2}@@{u}{k}\Jacobiellsnk^{2}@@{v}{k}}} | JacobiSN(u + v, k) = (JacobiSN(u, k)*JacobiCN(v, k)*JacobiDN(v, k)+ JacobiSN(v, k)*JacobiCN(u, k)*JacobiDN(u, k))/(1 - (k)^(2)* (JacobiSN(u, k))^(2)* (JacobiSN(v, k))^(2)) |
JacobiSN[u + v, (k)^2] == Divide[JacobiSN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[v, (k)^2]+ JacobiSN[v, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[u, (k)^2],1 - (k)^(2)* (JacobiSN[u, (k)^2])^(2)* (JacobiSN[v, (k)^2])^(2)] |
Successful | Aborted | - | Successful [Tested: 300] |
| 22.8.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@@{(u+v)}{k} = \frac{\Jacobiellcnk@@{u}{k}\Jacobiellcnk@@{v}{k}-\Jacobiellsnk@@{u}{k}\Jacobielldnk@@{u}{k}\Jacobiellsnk@@{v}{k}\Jacobielldnk@@{v}{k}}{1-k^{2}\Jacobiellsnk^{2}@@{u}{k}\Jacobiellsnk^{2}@@{v}{k}}} | JacobiCN(u + v, k) = (JacobiCN(u, k)*JacobiCN(v, k)- JacobiSN(u, k)*JacobiDN(u, k)*JacobiSN(v, k)*JacobiDN(v, k))/(1 - (k)^(2)* (JacobiSN(u, k))^(2)* (JacobiSN(v, k))^(2)) |
JacobiCN[u + v, (k)^2] == Divide[JacobiCN[u, (k)^2]*JacobiCN[v, (k)^2]- JacobiSN[u, (k)^2]*JacobiDN[u, (k)^2]*JacobiSN[v, (k)^2]*JacobiDN[v, (k)^2],1 - (k)^(2)* (JacobiSN[u, (k)^2])^(2)* (JacobiSN[v, (k)^2])^(2)] |
Successful | Aborted | - | Successful [Tested: 300] |
| 22.8.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@@{(u+v)}{k} = \frac{\Jacobielldnk@@{u}{k}\Jacobielldnk@@{v}{k}-k^{2}\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{u}{k}\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{v}{k}}{1-k^{2}\Jacobiellsnk^{2}@@{u}{k}\Jacobiellsnk^{2}@@{v}{k}}} | JacobiDN(u + v, k) = (JacobiDN(u, k)*JacobiDN(v, k)- (k)^(2)* JacobiSN(u, k)*JacobiCN(u, k)*JacobiSN(v, k)*JacobiCN(v, k))/(1 - (k)^(2)* (JacobiSN(u, k))^(2)* (JacobiSN(v, k))^(2)) |
JacobiDN[u + v, (k)^2] == Divide[JacobiDN[u, (k)^2]*JacobiDN[v, (k)^2]- (k)^(2)* JacobiSN[u, (k)^2]*JacobiCN[u, (k)^2]*JacobiSN[v, (k)^2]*JacobiCN[v, (k)^2],1 - (k)^(2)* (JacobiSN[u, (k)^2])^(2)* (JacobiSN[v, (k)^2])^(2)] |
Successful | Aborted | - | Successful [Tested: 300] |
| 22.8.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcdk@@{(u+v)}{k} = \frac{\Jacobiellcdk@@{u}{k}\Jacobiellcdk@@{v}{k}-{k^{\prime}}^{2}\Jacobiellsdk@@{u}{k}\Jacobiellndk@@{u}{k}\Jacobiellsdk@@{v}{k}\Jacobiellndk@@{v}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@@{u}{k}\Jacobiellsdk^{2}@@{v}{k}}} | JacobiCD(u + v, k) = (JacobiCD(u, k)*JacobiCD(v, k)-1 - (k)^(2)*JacobiSD(u, k)*JacobiND(u, k)*JacobiSD(v, k)*JacobiND(v, k))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(u, k))^(2)* (JacobiSD(v, k))^(2)) |
JacobiCD[u + v, (k)^2] == Divide[JacobiCD[u, (k)^2]*JacobiCD[v, (k)^2]-1 - (k)^(2)*JacobiSD[u, (k)^2]*JacobiND[u, (k)^2]*JacobiSD[v, (k)^2]*JacobiND[v, (k)^2],1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[u, (k)^2])^(2)* (JacobiSD[v, (k)^2])^(2)] |
Failure | Aborted | Failed [300 / 300] 300/300]: [[.6073373021+.4789879505*I <- {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 1}.5744703200+.1556450229*I <- {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[0.6073373022896961, 0.47898795042922426] <- {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.5744703197186243, 0.15564502146829437] <- {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.8.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsdk@@{(u+v)}{k} = \frac{\Jacobiellsdk@@{u}{k}\Jacobiellcdk@@{v}{k}\Jacobiellndk@@{v}{k}+\Jacobiellsdk@@{v}{k}\Jacobiellcdk@@{u}{k}\Jacobiellndk@@{u}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@@{u}{k}\Jacobiellsdk^{2}@@{v}{k}}} | JacobiSD(u + v, k) = (JacobiSD(u, k)*JacobiCD(v, k)*JacobiND(v, k)+ JacobiSD(v, k)*JacobiCD(u, k)*JacobiND(u, k))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(u, k))^(2)* (JacobiSD(v, k))^(2)) |
JacobiSD[u + v, (k)^2] == Divide[JacobiSD[u, (k)^2]*JacobiCD[v, (k)^2]*JacobiND[v, (k)^2]+ JacobiSD[v, (k)^2]*JacobiCD[u, (k)^2]*JacobiND[u, (k)^2],1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[u, (k)^2])^(2)* (JacobiSD[v, (k)^2])^(2)] |
Failure | Aborted | Failed [270 / 300] 270/300]: [[1.189544202+1.637439170*I <- {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 1}-.5756484648e-1+.8251147581*I <- {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [270 / 300]
{Complex[1.189544200468709, 1.6374391687321102] <- {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.05756484595277844, 0.825114758131751] <- {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.8.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellndk@@{(u+v)}{k} = \frac{\Jacobiellndk@@{u}{k}\Jacobiellndk@@{v}{k}+k^{2}\Jacobiellsdk@@{u}{k}\Jacobiellcdk@@{u}{k}\Jacobiellsdk@@{v}{k}\Jacobiellcdk@@{v}{k}}{1+k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{2}@@{u}{k}\Jacobiellsdk^{2}@@{v}{k}}} | JacobiND(u + v, k) = (JacobiND(u, k)*JacobiND(v, k)+ (k)^(2)* JacobiSD(u, k)*JacobiCD(u, k)*JacobiSD(v, k)*JacobiCD(v, k))/(1 + (k)^(2)*1 - (k)^(2)*(JacobiSD(u, k))^(2)* (JacobiSD(v, k))^(2)) |
JacobiND[u + v, (k)^2] == Divide[JacobiND[u, (k)^2]*JacobiND[v, (k)^2]+ (k)^(2)* JacobiSD[u, (k)^2]*JacobiCD[u, (k)^2]*JacobiSD[v, (k)^2]*JacobiCD[v, (k)^2],1 + (k)^(2)*1 - (k)^(2)*(JacobiSD[u, (k)^2])^(2)* (JacobiSD[v, (k)^2])^(2)] |
Failure | Aborted | Failed [300 / 300] 300/300]: [[1.247856974+1.526848242*I <- {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 1}-.1237018962-.8644962079e-1*I <- {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[1.2478569728519586, 1.5268482411210251] <- {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.1237018961558749, -0.0864496199922923] <- {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.8.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldck@@{(u+v)}{k} = \frac{\Jacobielldck@@{u}{k}\Jacobielldck@@{v}{k}+{k^{\prime}}^{2}\Jacobiellsck@@{u}{k}\Jacobiellnck@@{u}{k}\Jacobiellsck@@{v}{k}\Jacobiellnck@@{v}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{2}@@{u}{k}\Jacobiellsck^{2}@@{v}{k}}} | JacobiDC(u + v, k) = (JacobiDC(u, k)*JacobiDC(v, k)+1 - (k)^(2)*JacobiSC(u, k)*JacobiNC(u, k)*JacobiSC(v, k)*JacobiNC(v, k))/(1 -1 - (k)^(2)*(JacobiSC(u, k))^(2)* (JacobiSC(v, k))^(2)) |
JacobiDC[u + v, (k)^2] == Divide[JacobiDC[u, (k)^2]*JacobiDC[v, (k)^2]+1 - (k)^(2)*JacobiSC[u, (k)^2]*JacobiNC[u, (k)^2]*JacobiSC[v, (k)^2]*JacobiNC[v, (k)^2],1 -1 - (k)^(2)*(JacobiSC[u, (k)^2])^(2)* (JacobiSC[v, (k)^2])^(2)] |
Failure | Aborted | Failed [300 / 300] 300/300]: [[-1.456738398+.1506627644*I <- {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 1}-4.350355103-.3722352376e-1*I <- {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[-1.456738400104645, 0.15066276425673586] <- {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-4.350355102633989, -0.03722352327899177] <- {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.8.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellnck@@{(u+v)}{k} = \frac{\Jacobiellnck@@{u}{k}\Jacobiellnck@@{v}{k}+\Jacobiellsck@@{u}{k}\Jacobielldck@@{u}{k}\Jacobiellsck@@{v}{k}\Jacobielldck@@{v}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{2}@@{u}{k}\Jacobiellsck^{2}@@{v}{k}}} | JacobiNC(u + v, k) = (JacobiNC(u, k)*JacobiNC(v, k)+ JacobiSC(u, k)*JacobiDC(u, k)*JacobiSC(v, k)*JacobiDC(v, k))/(1 -1 - (k)^(2)*(JacobiSC(u, k))^(2)* (JacobiSC(v, k))^(2)) |
JacobiNC[u + v, (k)^2] == Divide[JacobiNC[u, (k)^2]*JacobiNC[v, (k)^2]+ JacobiSC[u, (k)^2]*JacobiDC[u, (k)^2]*JacobiSC[v, (k)^2]*JacobiDC[v, (k)^2],1 -1 - (k)^(2)*(JacobiSC[u, (k)^2])^(2)* (JacobiSC[v, (k)^2])^(2)] |
Failure | Aborted | Failed [300 / 300] 300/300]: [[1.356171111+.335718656*I <- {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 1}.3210452605+.1984107752*I <- {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[1.356171110076661, 0.3357186535359711] <- {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.3210452604978905, 0.19841077324251138] <- {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.8.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsck@@{(u+v)}{k} = \frac{\Jacobiellsck@@{u}{k}\Jacobielldck@@{v}{k}\Jacobiellnck@@{v}{k}+\Jacobiellsck@@{v}{k}\Jacobielldck@@{u}{k}\Jacobiellnck@@{u}{k}}{1-{k^{\prime}}^{2}\Jacobiellsck^{2}@@{u}{k}\Jacobiellsck^{2}@@{v}{k}}} | JacobiSC(u + v, k) = (JacobiSC(u, k)*JacobiDC(v, k)*JacobiNC(v, k)+ JacobiSC(v, k)*JacobiDC(u, k)*JacobiNC(u, k))/(1 -1 - (k)^(2)*(JacobiSC(u, k))^(2)* (JacobiSC(v, k))^(2)) |
JacobiSC[u + v, (k)^2] == Divide[JacobiSC[u, (k)^2]*JacobiDC[v, (k)^2]*JacobiNC[v, (k)^2]+ JacobiSC[v, (k)^2]*JacobiDC[u, (k)^2]*JacobiNC[u, (k)^2],1 -1 - (k)^(2)*(JacobiSC[u, (k)^2])^(2)* (JacobiSC[v, (k)^2])^(2)] |
Failure | Aborted | Failed [270 / 300] 270/300]: [[1.370082581+.423198902*I <- {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 1}.2742031773e-1-2.068263955*I <- {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [270 / 300]
{Complex[1.3700825790735573, 0.42319889849983916] <- {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.027420317388659004, -2.068263954207401] <- {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.8.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellnsk@@{(u+v)}{k} = \frac{\Jacobiellnsk@@{u}{k}\Jacobielldsk@@{v}{k}\Jacobiellcsk@@{v}{k}-\Jacobiellnsk@@{v}{k}\Jacobielldsk@@{u}{k}\Jacobiellcsk@@{u}{k}}{\Jacobiellcsk^{2}@@{v}{k}-\Jacobiellcsk^{2}@@{u}{k}}} | JacobiNS(u + v, k) = (JacobiNS(u, k)*JacobiDS(v, k)*JacobiCS(v, k)- JacobiNS(v, k)*JacobiDS(u, k)*JacobiCS(u, k))/((JacobiCS(v, k))^(2)- (JacobiCS(u, k))^(2)) |
JacobiNS[u + v, (k)^2] == Divide[JacobiNS[u, (k)^2]*JacobiDS[v, (k)^2]*JacobiCS[v, (k)^2]- JacobiNS[v, (k)^2]*JacobiDS[u, (k)^2]*JacobiCS[u, (k)^2],(JacobiCS[v, (k)^2])^(2)- (JacobiCS[u, (k)^2])^(2)] |
Successful | Aborted | - | Failed [60 / 300]
{Indeterminate <- {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.8.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldsk@@{(u+v)}{k} = \frac{\Jacobielldsk@@{u}{k}\Jacobiellcsk@@{v}{k}\Jacobiellnsk@@{v}{k}-\Jacobielldsk@@{v}{k}\Jacobiellcsk@@{u}{k}\Jacobiellnsk@@{u}{k}}{\Jacobiellcsk^{2}@@{v}{k}-\Jacobiellcsk^{2}@@{u}{k}}} | JacobiDS(u + v, k) = (JacobiDS(u, k)*JacobiCS(v, k)*JacobiNS(v, k)- JacobiDS(v, k)*JacobiCS(u, k)*JacobiNS(u, k))/((JacobiCS(v, k))^(2)- (JacobiCS(u, k))^(2)) |
JacobiDS[u + v, (k)^2] == Divide[JacobiDS[u, (k)^2]*JacobiCS[v, (k)^2]*JacobiNS[v, (k)^2]- JacobiDS[v, (k)^2]*JacobiCS[u, (k)^2]*JacobiNS[u, (k)^2],(JacobiCS[v, (k)^2])^(2)- (JacobiCS[u, (k)^2])^(2)] |
Successful | Aborted | - | Failed [60 / 300]
{Indeterminate <- {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.8.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcsk@@{(u+v)}{k} = \frac{\Jacobiellcsk@@{u}{k}\Jacobielldsk@@{v}{k}\Jacobiellnsk@@{v}{k}-\Jacobiellcsk@@{v}{k}\Jacobielldsk@@{u}{k}\Jacobiellnsk@@{u}{k}}{\Jacobiellcsk^{2}@@{v}{k}-\Jacobiellcsk^{2}@@{u}{k}}} | JacobiCS(u + v, k) = (JacobiCS(u, k)*JacobiDS(v, k)*JacobiNS(v, k)- JacobiCS(v, k)*JacobiDS(u, k)*JacobiNS(u, k))/((JacobiCS(v, k))^(2)- (JacobiCS(u, k))^(2)) |
JacobiCS[u + v, (k)^2] == Divide[JacobiCS[u, (k)^2]*JacobiDS[v, (k)^2]*JacobiNS[v, (k)^2]- JacobiCS[v, (k)^2]*JacobiDS[u, (k)^2]*JacobiNS[u, (k)^2],(JacobiCS[v, (k)^2])^(2)- (JacobiCS[u, (k)^2])^(2)] |
Successful | Aborted | - | Failed [60 / 300]
{Indeterminate <- {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.8.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@@{(u+v)}{k} = \frac{\Jacobiellsnk^{2}@@{u}{k}-\Jacobiellsnk^{2}@@{v}{k}}{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{v}{k}-\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{u}{k}}} | JacobiSN(u + v, k) = ((JacobiSN(u, k))^(2)- (JacobiSN(v, k))^(2))/(JacobiSN(u, k)*JacobiCN(v, k)*JacobiDN(v, k)- JacobiSN(v, k)*JacobiCN(u, k)*JacobiDN(u, k)) |
JacobiSN[u + v, (k)^2] == Divide[(JacobiSN[u, (k)^2])^(2)- (JacobiSN[v, (k)^2])^(2),JacobiSN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[v, (k)^2]- JacobiSN[v, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[u, (k)^2]] |
Successful | Aborted | - | Failed [30 / 300]
{Indeterminate <- {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.8.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@@{(u+v)}{k} = \frac{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{v}{k}+\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{u}{k}}{\Jacobiellcnk@@{u}{k}\Jacobiellcnk@@{v}{k}+\Jacobiellsnk@@{u}{k}\Jacobielldnk@@{u}{k}\Jacobiellsnk@@{v}{k}\Jacobielldnk@@{v}{k}}} | JacobiSN(u + v, k) = (JacobiSN(u, k)*JacobiCN(u, k)*JacobiDN(v, k)+ JacobiSN(v, k)*JacobiCN(v, k)*JacobiDN(u, k))/(JacobiCN(u, k)*JacobiCN(v, k)+ JacobiSN(u, k)*JacobiDN(u, k)*JacobiSN(v, k)*JacobiDN(v, k)) |
JacobiSN[u + v, (k)^2] == Divide[JacobiSN[u, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[v, (k)^2]+ JacobiSN[v, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[u, (k)^2],JacobiCN[u, (k)^2]*JacobiCN[v, (k)^2]+ JacobiSN[u, (k)^2]*JacobiDN[u, (k)^2]*JacobiSN[v, (k)^2]*JacobiDN[v, (k)^2]] |
Successful | Aborted | - | Successful [Tested: 300] |
| 22.8.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@@{(u+v)}{k} = \frac{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{v}{k}-\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{u}{k}}{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{v}{k}-\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{u}{k}}} | JacobiCN(u + v, k) = (JacobiSN(u, k)*JacobiCN(u, k)*JacobiDN(v, k)- JacobiSN(v, k)*JacobiCN(v, k)*JacobiDN(u, k))/(JacobiSN(u, k)*JacobiCN(v, k)*JacobiDN(v, k)- JacobiSN(v, k)*JacobiCN(u, k)*JacobiDN(u, k)) |
JacobiCN[u + v, (k)^2] == Divide[JacobiSN[u, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[v, (k)^2]- JacobiSN[v, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[u, (k)^2],JacobiSN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[v, (k)^2]- JacobiSN[v, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[u, (k)^2]] |
Successful | Aborted | - | Failed [30 / 300]
{Indeterminate <- {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.8.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@@{(u+v)}{k} = \frac{1-\Jacobiellsnk^{2}@@{u}{k}-\Jacobiellsnk^{2}@@{v}{k}+k^{2}\Jacobiellsnk^{2}@@{u}{k}\Jacobiellsnk^{2}@@{v}{k}}{\Jacobiellcnk@@{u}{k}\Jacobiellcnk@@{v}{k}+\Jacobiellsnk@@{u}{k}\Jacobielldnk@@{u}{k}\Jacobiellsnk@@{v}{k}\Jacobielldnk@@{v}{k}}} | JacobiCN(u + v, k) = (1 - (JacobiSN(u, k))^(2)- (JacobiSN(v, k))^(2)+ (k)^(2)* (JacobiSN(u, k))^(2)* (JacobiSN(v, k))^(2))/(JacobiCN(u, k)*JacobiCN(v, k)+ JacobiSN(u, k)*JacobiDN(u, k)*JacobiSN(v, k)*JacobiDN(v, k)) |
JacobiCN[u + v, (k)^2] == Divide[1 - (JacobiSN[u, (k)^2])^(2)- (JacobiSN[v, (k)^2])^(2)+ (k)^(2)* (JacobiSN[u, (k)^2])^(2)* (JacobiSN[v, (k)^2])^(2),JacobiCN[u, (k)^2]*JacobiCN[v, (k)^2]+ JacobiSN[u, (k)^2]*JacobiDN[u, (k)^2]*JacobiSN[v, (k)^2]*JacobiDN[v, (k)^2]] |
Successful | Aborted | - | Successful [Tested: 300] |
| 22.8.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@@{(u+v)}{k} = \frac{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{u}{k}-\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{v}{k}}{\Jacobiellsnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{v}{k}-\Jacobiellsnk@@{v}{k}\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{u}{k}}} | JacobiDN(u + v, k) = (JacobiSN(u, k)*JacobiCN(v, k)*JacobiDN(u, k)- JacobiSN(v, k)*JacobiCN(u, k)*JacobiDN(v, k))/(JacobiSN(u, k)*JacobiCN(v, k)*JacobiDN(v, k)- JacobiSN(v, k)*JacobiCN(u, k)*JacobiDN(u, k)) |
JacobiDN[u + v, (k)^2] == Divide[JacobiSN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[u, (k)^2]- JacobiSN[v, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[v, (k)^2],JacobiSN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[v, (k)^2]- JacobiSN[v, (k)^2]*JacobiCN[u, (k)^2]*JacobiDN[u, (k)^2]] |
Successful | Aborted | - | Failed [30 / 300]
{Indeterminate <- {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.8.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@@{(u+v)}{k} = \frac{\Jacobiellcnk@@{u}{k}\Jacobielldnk@@{u}{k}\Jacobiellcnk@@{v}{k}\Jacobielldnk@@{v}{k}+{k^{\prime}}^{2}\Jacobiellsnk@@{u}{k}\Jacobiellsnk@@{v}{k}}{\Jacobiellcnk@@{u}{k}\Jacobiellcnk@@{v}{k}+\Jacobiellsnk@@{u}{k}\Jacobielldnk@@{u}{k}\Jacobiellsnk@@{v}{k}\Jacobielldnk@@{v}{k}}} | JacobiDN(u + v, k) = (JacobiCN(u, k)*JacobiDN(u, k)*JacobiCN(v, k)*JacobiDN(v, k)+1 - (k)^(2)*JacobiSN(u, k)*JacobiSN(v, k))/(JacobiCN(u, k)*JacobiCN(v, k)+ JacobiSN(u, k)*JacobiDN(u, k)*JacobiSN(v, k)*JacobiDN(v, k)) |
JacobiDN[u + v, (k)^2] == Divide[JacobiCN[u, (k)^2]*JacobiDN[u, (k)^2]*JacobiCN[v, (k)^2]*JacobiDN[v, (k)^2]+1 - (k)^(2)*JacobiSN[u, (k)^2]*JacobiSN[v, (k)^2],JacobiCN[u, (k)^2]*JacobiCN[v, (k)^2]+ JacobiSN[u, (k)^2]*JacobiDN[u, (k)^2]*JacobiSN[v, (k)^2]*JacobiDN[v, (k)^2]] |
Failure | Aborted | Failed [300 / 300] 300/300]: [[-.6011182715+.1479228534*I <- {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 1}-2.889107517+1.386528377*I <- {u = 1/2*3^(1/2)+1/2*I, v = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[-0.6011182715762831, 0.14792285354183748] <- {Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-2.8891075280231666, 1.3865283695917823] <- {Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[v, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.8.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}+z_{2}+z_{3}+z_{4} = 0} | z[1]+ z[2]+ z[3]+ z[4] = 0 |
Subscript[z, 1]+ Subscript[z, 2]+ Subscript[z, 3]+ Subscript[z, 4] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.8.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {k^{\prime}}^{2}-{k^{\prime}}^{2}k^{2}\Jacobiellsnk@@{z_{1}}{k}\Jacobiellsnk@@{z_{2}}{k}\Jacobiellsnk@@{z_{3}}{k}\Jacobiellsnk@@{z_{4}}{k}+k^{2}\Jacobiellcnk@@{z_{1}}{k}\Jacobiellcnk@@{z_{2}}{k}\Jacobiellcnk@@{z_{3}}{k}\Jacobiellcnk@@{z_{4}}{k}-\Jacobielldnk@@{z_{1}}{k}\Jacobielldnk@@{z_{2}}{k}\Jacobielldnk@@{z_{3}}{k}\Jacobielldnk@@{z_{4}}{k} = 0} | 1 - (k)^(2)-1 - (k)^(2)*(k)^(2)* JacobiSN(z[1], k)*JacobiSN(z[2], k)*JacobiSN(z[3], k)*JacobiSN(z[4], k)+ (k)^(2)* JacobiCN(z[1], k)*JacobiCN(z[2], k)*JacobiCN(z[3], k)*JacobiCN(z[4], k)- JacobiDN(z[1], k)*JacobiDN(z[2], k)*JacobiDN(z[3], k)*JacobiDN(z[4], k) = 0 |
1 - (k)^(2)-1 - (k)^(2)*(k)^(2)* JacobiSN[Subscript[z, 1], (k)^2]*JacobiSN[Subscript[z, 2], (k)^2]*JacobiSN[Subscript[z, 3], (k)^2]*JacobiSN[Subscript[z, 4], (k)^2]+ (k)^(2)* JacobiCN[Subscript[z, 1], (k)^2]*JacobiCN[Subscript[z, 2], (k)^2]*JacobiCN[Subscript[z, 3], (k)^2]*JacobiCN[Subscript[z, 4], (k)^2]- JacobiDN[Subscript[z, 1], (k)^2]*JacobiDN[Subscript[z, 2], (k)^2]*JacobiDN[Subscript[z, 3], (k)^2]*JacobiDN[Subscript[z, 4], (k)^2] == 0 |
Failure | Failure | Failed [300 / 300] 300/300]: [[-1.174291399-.4389390377*I <- {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = 1/2*3^(1/2)+1/2*I, z[3] = 1/2*3^(1/2)+1/2*I, z[4] = 1/2*3^(1/2)+1/2*I, k = 1}-6.960363418+.5505072293*I <- {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = 1/2*3^(1/2)+1/2*I, z[3] = 1/2*3^(1/2)+1/2*I, z[4] = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [2 / 3]
{-3.0 <- {Rule[k, 2]}-8.0 <- {Rule[k, 3]} |
| 22.8.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}+z_{2}+z_{3}+z_{4} = 2\compellintKk@{k}} | z[1]+ z[2]+ z[3]+ z[4] = 2*EllipticK(k) |
Subscript[z, 1]+ Subscript[z, 2]+ Subscript[z, 3]+ Subscript[z, 4] == 2*EllipticK[(k)^2] |
Failure | Failure | Error | Failed [300 / 300]
{DirectedInfinity[] <- {Rule[k, 1], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.7783512603251586, 4.156515647499643] <- {Rule[k, 2], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.8.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}-z_{2} = z_{2}-z_{3}} | z[1]- z[2] = z[2]- z[3] |
Subscript[z, 1]- Subscript[z, 2] == Subscript[z, 2]- Subscript[z, 3] |
Failure | Failure | Failed [297 / 300] 297/300]: [[-1.366025404+.3660254040*I <- {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = 1/2*3^(1/2)+1/2*I, z[3] = -1/2+1/2*I*3^(1/2)}-.3660254040-1.366025404*I <- {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = 1/2*3^(1/2)+1/2*I, z[3] = 1/2-1/2*I*3^(1/2)} |
Failed [297 / 300]
{Complex[-1.3660254037844384, 0.36602540378443876] <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}Complex[-0.3660254037844386, -1.3660254037844386] <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]} |
| 22.8.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{2}-z_{3} = \tfrac{2}{3}\compellintKk@{k}} | z[2]- z[3] = (2)/(3)*EllipticK(k) |
Subscript[z, 2]- Subscript[z, 3] == Divide[2,3]*EllipticK[(k)^2] |
Failure | Failure | Error | Failed [300 / 300]
{DirectedInfinity[] <- {Rule[k, 1], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.561916784937532, 0.7188385491665478] <- {Rule[k, 2], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.8.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{1}-z_{2} = z_{2}-z_{3}} | z[1]- z[2] = z[2]- z[3] |
Subscript[z, 1]- Subscript[z, 2] == Subscript[z, 2]- Subscript[z, 3] |
Failure | Failure | Failed [297 / 300] 297/300]: [[-1.366025404+.3660254040*I <- {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = 1/2*3^(1/2)+1/2*I, z[3] = -1/2+1/2*I*3^(1/2)}-.3660254040-1.366025404*I <- {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = 1/2*3^(1/2)+1/2*I, z[3] = 1/2-1/2*I*3^(1/2)} |
Failed [297 / 300]
{Complex[-1.3660254037844384, 0.36602540378443876] <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}Complex[-0.3660254037844386, -1.3660254037844386] <- {Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]} |
| 22.8.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{2}-z_{3} = z_{3}-z_{4}} | z[2]- z[3] = z[3]- z[4] |
Subscript[z, 2]- Subscript[z, 3] == Subscript[z, 3]- Subscript[z, 4] |
Failure | Failure | Failed [297 / 300] 297/300]: [[-1.366025404+.3660254040*I <- {z[2] = 1/2*3^(1/2)+1/2*I, z[3] = 1/2*3^(1/2)+1/2*I, z[4] = -1/2+1/2*I*3^(1/2)}-.3660254040-1.366025404*I <- {z[2] = 1/2*3^(1/2)+1/2*I, z[3] = 1/2*3^(1/2)+1/2*I, z[4] = 1/2-1/2*I*3^(1/2)} |
Failed [297 / 300]
{Complex[-1.3660254037844384, 0.36602540378443876] <- {Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}Complex[-0.3660254037844386, -1.3660254037844386] <- {Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]} |
| 22.8.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{3}-z_{4} = \tfrac{1}{2}\compellintKk@{k}} | z[3]- z[4] = (1)/(2)*EllipticK(k) |
Subscript[z, 3]- Subscript[z, 4] == Divide[1,2]*EllipticK[(k)^2] |
Failure | Failure | Error | Failed [300 / 300]
{DirectedInfinity[] <- {Rule[k, 1], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.42143758870314907, 0.5391289118749109] <- {Rule[k, 2], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.8.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@@{z_{1}}{k}\Jacobielldnk@@{z_{3}}{k} = \Jacobielldnk@@{z_{2}}{k}\Jacobielldnk@@{z_{4}}{k}} | JacobiDN(z[1], k)*JacobiDN(z[3], k) = JacobiDN(z[2], k)*JacobiDN(z[4], k) |
JacobiDN[Subscript[z, 1], (k)^2]*JacobiDN[Subscript[z, 3], (k)^2] == JacobiDN[Subscript[z, 2], (k)^2]*JacobiDN[Subscript[z, 4], (k)^2] |
Failure | Failure | Failed [240 / 300] 240/300]: [[-.4756423320-.5071574760*I <- {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = 1/2*3^(1/2)+1/2*I, z[3] = 1/2*3^(1/2)+1/2*I, z[4] = -1/2+1/2*I*3^(1/2), k = 1}-2.554390475+.7152903744*I <- {z[1] = 1/2*3^(1/2)+1/2*I, z[2] = 1/2*3^(1/2)+1/2*I, z[3] = 1/2*3^(1/2)+1/2*I, z[4] = -1/2+1/2*I*3^(1/2), k = 2} |
Failed [240 / 300]
{Complex[-0.475642332072964, -0.5071574758549496] <- {Rule[k, 1], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}Complex[-2.5543904750381285, 0.715290373196519] <- {Rule[k, 2], Rule[Subscript[z, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 22.8.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@@{z_{2}}{k}\Jacobielldnk@@{z_{4}}{k} = k^{\prime}} | JacobiDN(z[2], k)*JacobiDN(z[4], k) = sqrt(1 - (k)^(2)) |
JacobiDN[Subscript[z, 2], (k)^2]*JacobiDN[Subscript[z, 4], (k)^2] == Sqrt[1 - (k)^(2)] |
Failure | Failure | Failed [300 / 300] 300/300]: [[.4314194118-.3859954480*I <- {z[2] = 1/2*3^(1/2)+1/2*I, z[4] = 1/2*3^(1/2)+1/2*I, k = 1}-.8474767071-1.646914265*I <- {z[2] = 1/2*3^(1/2)+1/2*I, z[4] = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[0.4314194120331003, -0.3859954480737353] <- {Rule[k, 1], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.8474767070969642, -1.6469142655565594] <- {Rule[k, 2], Rule[Subscript[z, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[z, 4], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.9.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{m,p}^{(2)} = \Jacobiellsnk@{z+2p^{-1}(m-1)\compellintKk@{k}}{k}} | (s[m , p])^(2) = JacobiSN(z + 2*(p)^(- 1)*(m - 1)* EllipticK(k), k) |
(Subscript[s, m , p])^(2) == JacobiSN[z + 2*(p)^(- 1)*(m - 1)* EllipticK[(k)^2], (k)^2] |
Failure | Failure | Error | Failed [300 / 300]
{Indeterminate <- {Rule[k, 1], Rule[m, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[k, 1], Rule[m, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.9.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{m,p}^{(2)} = \Jacobiellcnk@{z+2p^{-1}(m-1)\compellintKk@{k}}{k}} | (c[m , p])^(2) = JacobiCN(z + 2*(p)^(- 1)*(m - 1)* EllipticK(k), k) |
(Subscript[c, m , p])^(2) == JacobiCN[z + 2*(p)^(- 1)*(m - 1)* EllipticK[(k)^2], (k)^2] |
Failure | Failure | Error | Failed [300 / 300]
{Indeterminate <- {Rule[k, 1], Rule[m, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[k, 1], Rule[m, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.9.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d_{m,p}^{(2)} = \Jacobielldnk@{z+2p^{-1}(m-1)\compellintKk@{k}}{k}} | (d[m , p])^(2) = JacobiDN(z + 2*(p)^(- 1)*(m - 1)* EllipticK(k), k) |
(Subscript[d, m , p])^(2) == JacobiDN[z + 2*(p)^(- 1)*(m - 1)* EllipticK[(k)^2], (k)^2] |
Failure | Failure | Error | Failed [300 / 300]
{Indeterminate <- {Rule[k, 1], Rule[m, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[d, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[k, 1], Rule[m, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[d, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.9.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{m,p}^{(4)} = \Jacobiellsnk@{z+4p^{-1}(m-1)\compellintKk@{k}}{k}} | (s[m , p])^(4) = JacobiSN(z + 4*(p)^(- 1)*(m - 1)* EllipticK(k), k) |
(Subscript[s, m , p])^(4) == JacobiSN[z + 4*(p)^(- 1)*(m - 1)* EllipticK[(k)^2], (k)^2] |
Failure | Failure | Error | Failed [300 / 300]
{Indeterminate <- {Rule[k, 1], Rule[m, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[k, 1], Rule[m, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[s, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.9.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{m,p}^{(4)} = \Jacobiellcnk@{z+4p^{-1}(m-1)\compellintKk@{k}}{k}} | (c[m , p])^(4) = JacobiCN(z + 4*(p)^(- 1)*(m - 1)* EllipticK(k), k) |
(Subscript[c, m , p])^(4) == JacobiCN[z + 4*(p)^(- 1)*(m - 1)* EllipticK[(k)^2], (k)^2] |
Failure | Failure | Error | Failed [300 / 300]
{Indeterminate <- {Rule[k, 1], Rule[m, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[k, 1], Rule[m, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.9.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d_{m,p}^{(4)} = \Jacobielldnk@{z+4p^{-1}(m-1)\compellintKk@{k}}{k}} | (d[m , p])^(4) = JacobiDN(z + 4*(p)^(- 1)*(m - 1)* EllipticK(k), k) |
(Subscript[d, m , p])^(4) == JacobiDN[z + 4*(p)^(- 1)*(m - 1)* EllipticK[(k)^2], (k)^2] |
Failure | Failure | Error | Failed [300 / 300]
{Indeterminate <- {Rule[k, 1], Rule[m, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[d, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[k, 1], Rule[m, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[d, m, p], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.9.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{1,3}^{(4)}s_{2,3}^{(4)}+s_{2,3}^{(4)}s_{3,3}^{(4)}+s_{3,3}^{(4)}s_{1,3}^{(4)} = \frac{\kappa^{2}-1}{k^{2}}} | (s[1 , 3])^(4)*(s[2 , 3])^(4)+ (s[2 , 3])^(4)*(s[3 , 3])^(4)+ (s[3 , 3])^(4)*(s[1 , 3])^(4) = ((kappa)^(2)- 1)/((k)^(2)) |
(Subscript[s, 1 , 3])^(4)*(Subscript[s, 2 , 3])^(4)+ (Subscript[s, 2 , 3])^(4)*(Subscript[s, 3 , 3])^(4)+ (Subscript[s, 3 , 3])^(4)*(Subscript[s, 1 , 3])^(4) == Divide[\[Kappa]^(2)- 1,(k)^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.9.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{1,3}^{(4)}c_{2,3}^{(4)}+c_{2,3}^{(4)}c_{3,3}^{(4)}+c_{3,3}^{(4)}c_{1,3}^{(4)} = -\frac{\kappa(\kappa+2)}{(1+\kappa)^{2}}} | (c[1 , 3])^(4)*(c[2 , 3])^(4)+ (c[2 , 3])^(4)*(c[3 , 3])^(4)+ (c[3 , 3])^(4)*(c[1 , 3])^(4) = -(kappa*(kappa + 2))/((1 + kappa)^(2)) |
(Subscript[c, 1 , 3])^(4)*(Subscript[c, 2 , 3])^(4)+ (Subscript[c, 2 , 3])^(4)*(Subscript[c, 3 , 3])^(4)+ (Subscript[c, 3 , 3])^(4)*(Subscript[c, 1 , 3])^(4) == -Divide[\[Kappa]*(\[Kappa]+ 2),(1 + \[Kappa])^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.9.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d_{1,3}^{(2)}d_{2,3}^{(2)}+d_{2,3}^{(2)}d_{3,3}^{(2)}+d_{3,3}^{(2)}d_{1,3}^{(2)} = d_{1,3}^{(4)}d_{2,3}^{(4)}+d_{2,3}^{(4)}d_{3,3}^{(4)}+d_{3,3}^{(4)}d_{1,3}^{(4)}} | (d[1 , 3])^(2)*(d[2 , 3])^(2)+ (d[2 , 3])^(2)*(d[3 , 3])^(2)+ (d[3 , 3])^(2)*(d[1 , 3])^(2) = (d[1 , 3])^(4)*(d[2 , 3])^(4)+ (d[2 , 3])^(4)*(d[3 , 3])^(4)+ (d[3 , 3])^(4)*(d[1 , 3])^(4) |
(Subscript[d, 1 , 3])^(2)*(Subscript[d, 2 , 3])^(2)+ (Subscript[d, 2 , 3])^(2)*(Subscript[d, 3 , 3])^(2)+ (Subscript[d, 3 , 3])^(2)*(Subscript[d, 1 , 3])^(2) == (Subscript[d, 1 , 3])^(4)*(Subscript[d, 2 , 3])^(4)+ (Subscript[d, 2 , 3])^(4)*(Subscript[d, 3 , 3])^(4)+ (Subscript[d, 3 , 3])^(4)*(Subscript[d, 1 , 3])^(4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.9.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(d_{1,2}^{(2)}\right)^{2}d_{2,2}^{(2)}+\left(d_{2,2}^{(2)}\right)^{2}d_{1,2}^{(2)} = k^{\prime}\left(d_{1,2}^{(2)}+ d_{2,2}^{(2)}\right)} | (d(d[1 , 2])^(2))^(2)* (d[2 , 2])^(2)(d(d[2 , 2])^(2))^(2)* (d[1 , 2])^(2) (d(d[1 , 2])^(2)+ d(d[2 , 2])^(2)) |
(d(Subscript[d, 1 , 2])^(2))^(2)* (Subscript[d, 2 , 2])^(2)(d(Subscript[d, 2 , 2])^(2))^(2)* (Subscript[d, 1 , 2])^(2) (d(Subscript[d, 1 , 2])^(2)+ d(Subscript[d, 2 , 2])^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.9.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{1,2}^{(2)}s_{1,2}^{(2)}d_{2,2}^{(2)}+c_{2,2}^{(2)}s_{2,2}^{(2)}d_{1,2}^{(2)} = 0} | (c[1 , 2])^(2)*(s[1 , 2])^(2)*(d[2 , 2])^(2)+ (c[2 , 2])^(2)*(s[2 , 2])^(2)*(d[1 , 2])^(2) = 0 |
(Subscript[c, 1 , 2])^(2)*(Subscript[s, 1 , 2])^(2)*(Subscript[d, 2 , 2])^(2)+ (Subscript[c, 2 , 2])^(2)*(Subscript[s, 2 , 2])^(2)*(Subscript[d, 1 , 2])^(2) == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.9.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{1,3}^{(4)}s_{2,3}^{(4)}s_{3,3}^{(4)} = -\frac{1}{1-\kappa^{2}}\left(s_{1,3}^{(4)}+s_{2,3}^{(4)}+s_{3,3}^{(4)}\right)} | (s[1 , 3])^(4)*(s[2 , 3])^(4)*(s[3 , 3])^(4) (s(s[1 , 3])^(4)+ s(s[2 , 3])^(4)+ s(s[3 , 3])^(4)) |
(Subscript[s, 1 , 3])^(4)*(Subscript[s, 2 , 3])^(4)*(Subscript[s, 3 , 3])^(4) (s(Subscript[s, 1 , 3])^(4)+ s(Subscript[s, 2 , 3])^(4)+ s(Subscript[s, 3 , 3])^(4)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.9.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{1,3}^{(4)}c_{2,3}^{(4)}c_{3,3}^{(4)} = \frac{\kappa^{2}}{1-\kappa^{2}}\left(c_{1,3}^{(4)}+c_{2,3}^{(4)}+c_{3,3}^{(4)}\right)} | (c[1 , 3])^(4)*(c[2 , 3])^(4)*(c(c[1 , 3])^(4)+ c(c[2 , 3])^(4)+ c(c[3 , 3])^(4)) |
(Subscript[c, 1 , 3])^(4)*(Subscript[c, 2 , 3])^(4)*(c(Subscript[c, 1 , 3])^(4)+ c(Subscript[c, 2 , 3])^(4)+ c(Subscript[c, 3 , 3])^(4)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.9.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d_{1,3}^{(2)}d_{2,3}^{(2)}d_{3,3}^{(2)} = \frac{\kappa^{2}+k^{2}-1}{1-\kappa^{2}}\left(d_{1,3}^{(2)}+d_{2,3}^{(2)}+d_{3,3}^{(2)}\right)} | (d[1 , 3])^(2)*(d[2 , 3])^(2)*(d(d[1 , 3])^(2)+ d(d[2 , 3])^(2)+ d(d[3 , 3])^(2)) |
(Subscript[d, 1 , 3])^(2)*(Subscript[d, 2 , 3])^(2)*(d(Subscript[d, 1 , 3])^(2)+ d(Subscript[d, 2 , 3])^(2)+ d(Subscript[d, 3 , 3])^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.9.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{1,3}^{(4)}c_{2,3}^{(4)}c_{3,3}^{(4)}+s_{2,3}^{(4)}c_{3,3}^{(4)}c_{1,3}^{(4)}+s_{3,3}^{(4)}c_{1,3}^{(4)}c_{2,3}^{(4)} = \frac{\kappa(\kappa+2)}{1-\kappa^{2}}\left(s_{1,3}^{(4)}+s_{2,3}^{(4)}+s_{3,3}^{(4)}\right)} | (s[1 , 3])^(4)*(c[2 , 3])^(4)*(c[3 , 3])^(4)+ (s[2 , 3])^(4)*(c[3 , 3])^(4)*(c[1 , 3])^(4)+ (s[3 , 3])^(4)*(c[1 , 3])^(4)*(s(s[1 , 3])^(4)+ s(s[2 , 3])^(4)+ s(s[3 , 3])^(4)) |
(Subscript[s, 1 , 3])^(4)*(Subscript[c, 2 , 3])^(4)*(Subscript[c, 3 , 3])^(4)+ (Subscript[s, 2 , 3])^(4)*(Subscript[c, 3 , 3])^(4)*(Subscript[c, 1 , 3])^(4)+ (Subscript[s, 3 , 3])^(4)*(Subscript[c, 1 , 3])^(4)*(s(Subscript[s, 1 , 3])^(4)+ s(Subscript[s, 2 , 3])^(4)+ s(Subscript[s, 3 , 3])^(4)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.9.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d_{1,4}^{(2)}d_{2,4}^{(2)}d_{3,4}^{(2)}+ d_{2,4}^{(2)}d_{3,4}^{(2)}d_{4,4}^{(2)}+d_{3,4}^{(2)}d_{4,4}^{(2)}d_{1,4}^{(2)}+ d_{4,4}^{(2)}d_{1,4}^{(2)}d_{2,4}^{(2)} = k^{\prime}{\left(+ d_{1,4}^{(2)}+d_{2,4}^{(2)}+ d_{3,4}^{(2)}+d_{4,4}^{(2)}\right)}} | (d[1 , 4])^(2)*(d[2 , 4])^(2)*(d[3 , 4])^(2)+ (d[2 , 4])^(2)*(d[3 , 4])^(2)*(d[4 , 4])^(2)+ (d[3 , 4])^(2)*(d[4 , 4])^(2)*(d[1 , 4])^(2)+ (d[4 , 4])^(2)*(+ d(d[1 , 4])^(2)+ d(d[2 , 4])^(2)+ d(d[3 , 4])^(2)+ d(d[4 , 4])^(2)) |
(Subscript[d, 1 , 4])^(2)*(Subscript[d, 2 , 4])^(2)*(Subscript[d, 3 , 4])^(2)+ (Subscript[d, 2 , 4])^(2)*(Subscript[d, 3 , 4])^(2)*(Subscript[d, 4 , 4])^(2)+ (Subscript[d, 3 , 4])^(2)*(Subscript[d, 4 , 4])^(2)*(Subscript[d, 1 , 4])^(2)+ (Subscript[d, 4 , 4])^(2)*(+ d(Subscript[d, 1 , 4])^(2)+ d(Subscript[d, 2 , 4])^(2)+ d(Subscript[d, 3 , 4])^(2)+ d(Subscript[d, 4 , 4])^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.9.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(d_{1,4}^{(2)}\right)^{2}d_{3,4}^{(2)}+\left(d_{2,4}^{(2)}\right)^{2}d_{4,4}^{(2)}+\left(d_{3,4}^{(2)}\right)^{2}d_{1,4}^{(2)}+\left(d_{4,4}^{(2)}\right)^{2}d_{2,4}^{(2)} = k^{\prime}{\left(d_{1,4}^{(2)}+ d_{2,4}^{(2)}+d_{3,4}^{(2)}+ d_{4,4}^{(2)}\right)}} | (d(d[1 , 4])^(2))^(2)* (d[3 , 4])^(2)(d(d[2 , 4])^(2))^(2)* (d[4 , 4])^(2)(d(d[3 , 4])^(2))^(2)* (d[1 , 4])^(2)(d(d[1 , 4])^(2)+ d(d[2 , 4])^(2)+ d(d[3 , 4])^(2)+ d(d[4 , 4])^(2)) |
(d(Subscript[d, 1 , 4])^(2))^(2)* (Subscript[d, 3 , 4])^(2)(d(Subscript[d, 2 , 4])^(2))^(2)* (Subscript[d, 4 , 4])^(2)(d(Subscript[d, 3 , 4])^(2))^(2)* (Subscript[d, 1 , 4])^(2)(d(Subscript[d, 1 , 4])^(2)+ d(Subscript[d, 2 , 4])^(2)+ d(Subscript[d, 3 , 4])^(2)+ d(Subscript[d, 4 , 4])^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.9.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{1,4}^{(2)}s_{1,4}^{(2)}d_{3,4}^{(2)}+c_{3,4}^{(2)}s_{3,4}^{(2)}d_{1,4}^{(2)} = c_{2,4}^{(2)}s_{2,4}^{(2)}d_{4,4}^{(2)}+c_{4,4}^{(2)}s_{4,4}^{(2)}d_{2,4}^{(2)}} | (c[1 , 4])^(2)*(s[1 , 4])^(2)*(d[3 , 4])^(2)+ (c[3 , 4])^(2)*(s[3 , 4])^(2)*(d[1 , 4])^(2) = (c[2 , 4])^(2)*(s[2 , 4])^(2)*(d[4 , 4])^(2)+ (c[4 , 4])^(2)*(s[4 , 4])^(2)*(d[2 , 4])^(2) |
(Subscript[c, 1 , 4])^(2)*(Subscript[s, 1 , 4])^(2)*(Subscript[d, 3 , 4])^(2)+ (Subscript[c, 3 , 4])^(2)*(Subscript[s, 3 , 4])^(2)*(Subscript[d, 1 , 4])^(2) == (Subscript[c, 2 , 4])^(2)*(Subscript[s, 2 , 4])^(2)*(Subscript[d, 4 , 4])^(2)+ (Subscript[c, 4 , 4])^(2)*(Subscript[s, 4 , 4])^(2)*(Subscript[d, 2 , 4])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.9.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(d_{1,2}^{(2)}\right)^{3}d_{2,2}^{(2)}+\left(d_{2,2}^{(2)}\right)^{3}d_{1,2}^{(2)} = k^{\prime}\left(\left(d_{1,2}^{(2)}\right)^{2}+\left(d_{2,2}^{(2)}\right)^{2}\right)} | (d(d[1 , 2])^(2))^(3)* (d[2 , 2])^(2)(d(d[2 , 2])^(2))^(3)* (d[1 , 2])^(2) ((d(d[1 , 2])^(2))^(2)+(d(d[2 , 2])^(2))^(2)) |
(d(Subscript[d, 1 , 2])^(2))^(3)* (Subscript[d, 2 , 2])^(2)(d(Subscript[d, 2 , 2])^(2))^(3)* (Subscript[d, 1 , 2])^(2) ((d(Subscript[d, 1 , 2])^(2))^(2)+(d(Subscript[d, 2 , 2])^(2))^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.9.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2}c_{1,2}^{(2)}s_{1,2}^{(2)}c_{2,2}^{(2)}s_{2,2}^{(2)} = k^{\prime}\left(1-\left(s_{1,2}^{(2)}\right)^{2}-\left(s_{2,2}^{(2)}\right)^{2}\right)} | (k)^(2)* (c[1 , 2])^(2)*(s[1 , 2])^(2)*(c[2 , 2])^(2)*(s[2 , 2])^(2) (1 -(s(s[1 , 2])^(2))^(2)-(s(s[2 , 2])^(2))^(2)) |
(k)^(2)* (Subscript[c, 1 , 2])^(2)*(Subscript[s, 1 , 2])^(2)*(Subscript[c, 2 , 2])^(2)*(Subscript[s, 2 , 2])^(2) (1 -(s(Subscript[s, 1 , 2])^(2))^(2)-(s(Subscript[s, 2 , 2])^(2))^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.9.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{1,3}^{(2)}c_{1,3}^{(2)}d_{2,3}^{(2)}d_{3,3}^{(2)}+s_{2,3}^{(2)}c_{2,3}^{(2)}d_{3,3}^{(2)}d_{1,3}^{(2)}+s_{3,3}^{(2)}c_{3,3}^{(2)}d_{1,3}^{(2)}d_{2,3}^{(2)} = \frac{\kappa^{2}+k^{2}-1}{1-\kappa^{2}}\left(s_{1,3}^{(2)}c_{1,3}^{(2)}+s_{2,3}^{(2)}c_{2,3}^{(2)}+s_{3,3}^{(2)}c_{3,3}^{(2)}\right)} | (s[1 , 3])^(2)*(c[1 , 3])^(2)*(d[2 , 3])^(2)*(d[3 , 3])^(2)+ (s[2 , 3])^(2)*(c[2 , 3])^(2)*(d[3 , 3])^(2)*(d[1 , 3])^(2)+ (s(s[1 , 3])^(2)*c(c[1 , 3])^(2)+ s(s[2 , 3])^(2)*c(c[2 , 3])^(2)+ s(s[3 , 3])^(2)*c(c[3 , 3])^(2)) |
(Subscript[s, 1 , 3])^(2)*(Subscript[c, 1 , 3])^(2)*(Subscript[d, 2 , 3])^(2)*(Subscript[d, 3 , 3])^(2)+ (Subscript[s, 2 , 3])^(2)*(Subscript[c, 2 , 3])^(2)*(Subscript[d, 3 , 3])^(2)*(Subscript[d, 1 , 3])^(2)+ (s(Subscript[s, 1 , 3])^(2)*c(Subscript[c, 1 , 3])^(2)+ s(Subscript[s, 2 , 3])^(2)*c(Subscript[c, 2 , 3])^(2)+ s(Subscript[s, 3 , 3])^(2)*c(Subscript[c, 3 , 3])^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.9.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s_{1,3}^{(4)}d_{1,3}^{(4)}c_{2,3}^{(4)}c_{3,3}^{(4)}+s_{2,3}^{(4)}d_{2,3}^{(4)}c_{3,3}^{(4)}c_{1,3}^{(4)}+s_{3,3}^{(4)}d_{3,3}^{(4)}c_{1,3}^{(4)}c_{2,3}^{(4)} = \frac{\kappa^{2}}{1-\kappa^{2}}\left(s_{1,3}^{(4)}d_{1,3}^{(4)}+s_{2,3}^{(4)}d_{2,3}^{(4)}+s_{2,3}^{(4)}d_{2,3}^{(4)}\right)} | (s[1 , 3])^(4)*(d[1 , 3])^(4)*(c[2 , 3])^(4)*(c[3 , 3])^(4)+ (s[2 , 3])^(4)*(d[2 , 3])^(4)*(c[3 , 3])^(4)*(c[1 , 3])^(4)+ (s(s[1 , 3])^(4)*d(d[1 , 3])^(4)+ s(s[2 , 3])^(4)*d(d[2 , 3])^(4)+ s(s[2 , 3])^(4)*d(d[2 , 3])^(4)) |
(Subscript[s, 1 , 3])^(4)*(Subscript[d, 1 , 3])^(4)*(Subscript[c, 2 , 3])^(4)*(Subscript[c, 3 , 3])^(4)+ (Subscript[s, 2 , 3])^(4)*(Subscript[d, 2 , 3])^(4)*(Subscript[c, 3 , 3])^(4)*(Subscript[c, 1 , 3])^(4)+ (s(Subscript[s, 1 , 3])^(4)*d(Subscript[d, 1 , 3])^(4)+ s(Subscript[s, 2 , 3])^(4)*d(Subscript[d, 2 , 3])^(4)+ s(Subscript[s, 2 , 3])^(4)*d(Subscript[d, 2 , 3])^(4)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.11.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}} | JacobiSN(z, k) = (2*Pi)/(K*k)*sum(((q)^(n +(1)/(2))* sin((2*n + 1)* zeta))/(1 - (q)^(2*n + 1)), n = 0..infinity) |
JacobiSN[z, (k)^2] == Divide[2*Pi,K*k]*Sum[Divide[(q)^(n +Divide[1,2])* Sin[(2*n + 1)* \[Zeta]],1 - (q)^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.11.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}} | JacobiCN(z, k) = (2*Pi)/(K*k)*sum(((q)^(n +(1)/(2))* cos((2*n + 1)* zeta))/(1 + (q)^(2*n + 1)), n = 0..infinity) |
JacobiCN[z, (k)^2] == Divide[2*Pi,K*k]*Sum[Divide[(q)^(n +Divide[1,2])* Cos[(2*n + 1)* \[Zeta]],1 + (q)^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.11.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{z}{k} = \frac{\pi}{2K}+\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{n}\cos@{2n\zeta}}{1+q^{2n}}} | JacobiDN(z, k) = (Pi)/(2*EllipticK(k))+(2*Pi)/(EllipticK(k))*sum(((q)^(n)* cos(2*n*zeta))/(1 + (q)^(2*n)), n = 1..infinity) |
JacobiDN[z, (k)^2] == Divide[Pi,2*EllipticK[(k)^2]]+Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(q)^(n)* Cos[2*n*\[Zeta]],1 + (q)^(2*n)], {n, 1, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.11.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcdk@{z}{k} = \frac{2\pi}{Kk}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}} | JacobiCD(z, k) = (2*Pi)/(K*k)*sum(((- 1)^(n)* (q)^(n +(1)/(2))* cos((2*n + 1)* zeta))/(1 - (q)^(2*n + 1)), n = 0..infinity) |
JacobiCD[z, (k)^2] == Divide[2*Pi,K*k]*Sum[Divide[(- 1)^(n)* (q)^(n +Divide[1,2])* Cos[(2*n + 1)* \[Zeta]],1 - (q)^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.11.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsdk@{z}{k} = \frac{2\pi}{Kkk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{n+\frac{1}{2}}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}} | JacobiSD(z, k) = (2*Pi)/(K*k*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)* (q)^(n +(1)/(2))* sin((2*n + 1)* zeta))/(1 + (q)^(2*n + 1)), n = 0..infinity) |
JacobiSD[z, (k)^2] == Divide[2*Pi,K*k*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)* (q)^(n +Divide[1,2])* Sin[(2*n + 1)* \[Zeta]],1 + (q)^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.11.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellndk@{z}{k} = \frac{\pi}{2Kk^{\prime}}+\frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{n}\cos@{2n\zeta}}{1+q^{2n}}} | JacobiND(z, k) = (Pi)/(2*EllipticK(k)*sqrt(1 - (k)^(2)))+(2*Pi)/(EllipticK(k)*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)* (q)^(n)* cos(2*n*zeta))/(1 + (q)^(2*n)), n = 1..infinity) |
JacobiND[z, (k)^2] == Divide[Pi,2*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]+Divide[2*Pi,EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)* (q)^(n)* Cos[2*n*\[Zeta]],1 + (q)^(2*n)], {n, 1, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.11.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellnsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1-q^{2n+1}}} | JacobiNS(z, k)-(Pi)/(2*EllipticK(k))*csc(zeta) = (2*Pi)/(EllipticK(k))*sum(((q)^(2*n + 1)* sin((2*n + 1)* zeta))/(1 - (q)^(2*n + 1)), n = 0..infinity) |
JacobiNS[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Csc[\[Zeta]] == Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(q)^(2*n + 1)* Sin[(2*n + 1)* \[Zeta]],1 - (q)^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.11.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldsk@{z}{k}-\frac{\pi}{2K}\csc@@{\zeta} = -\frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{q^{2n+1}\sin@{(2n+1)\zeta}}{1+q^{2n+1}}} | JacobiDS(z, k)-(Pi)/(2*EllipticK(k))*csc(zeta) = -(2*Pi)/(EllipticK(k))*sum(((q)^(2*n + 1)* sin((2*n + 1)* zeta))/(1 + (q)^(2*n + 1)), n = 0..infinity) |
JacobiDS[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Csc[\[Zeta]] == -Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(q)^(2*n + 1)* Sin[(2*n + 1)* \[Zeta]],1 + (q)^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.11.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcsk@{z}{k}-\frac{\pi}{2K}\cot@@{\zeta} = -\frac{2\pi}{K}\sum_{n=1}^{\infty}\frac{q^{2n}\sin@{2n\zeta}}{1+q^{2n}}} | JacobiCS(z, k)-(Pi)/(2*EllipticK(k))*cot(zeta) = -(2*Pi)/(EllipticK(k))*sum(((q)^(2*n)* sin(2*n*zeta))/(1 + (q)^(2*n)), n = 1..infinity) |
JacobiCS[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Cot[\[Zeta]] == -Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(q)^(2*n)* Sin[2*n*\[Zeta]],1 + (q)^(2*n)], {n, 1, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.11.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldck@{z}{k}-\frac{\pi}{2K}\sec@@{\zeta} = \frac{2\pi}{K}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1-q^{2n+1}}} | JacobiDC(z, k)-(Pi)/(2*EllipticK(k))*sec(zeta) = (2*Pi)/(EllipticK(k))*sum(((- 1)^(n)* (q)^(2*n + 1)* cos((2*n + 1)* zeta))/(1 - (q)^(2*n + 1)), n = 0..infinity) |
JacobiDC[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]]*Sec[\[Zeta]] == Divide[2*Pi,EllipticK[(k)^2]]*Sum[Divide[(- 1)^(n)* (q)^(2*n + 1)* Cos[(2*n + 1)* \[Zeta]],1 - (q)^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.11.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellnck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\sec@@{\zeta} = -\frac{2\pi}{Kk^{\prime}}\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{2n+1}\cos@{(2n+1)\zeta}}{1+q^{2n+1}}} | JacobiNC(z, k)-(Pi)/(2*EllipticK(k)*sqrt(1 - (k)^(2)))*sec(zeta) = -(2*Pi)/(EllipticK(k)*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)* (q)^(2*n + 1)* cos((2*n + 1)* zeta))/(1 + (q)^(2*n + 1)), n = 0..infinity) |
JacobiNC[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Sec[\[Zeta]] == -Divide[2*Pi,EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)* (q)^(2*n + 1)* Cos[(2*n + 1)* \[Zeta]],1 + (q)^(2*n + 1)], {n, 0, Infinity}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.11.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsck@{z}{k}-\frac{\pi}{2Kk^{\prime}}\tan@@{\zeta} = \frac{2\pi}{Kk^{\prime}}\sum_{n=1}^{\infty}\frac{(-1)^{n}q^{2n}\sin@{2n\zeta}}{1+q^{2n}}} | JacobiSC(z, k)-(Pi)/(2*EllipticK(k)*sqrt(1 - (k)^(2)))*tan(zeta) = (2*Pi)/(EllipticK(k)*sqrt(1 - (k)^(2)))*sum(((- 1)^(n)* (q)^(2*n)* sin(2*n*zeta))/(1 + (q)^(2*n)), n = 1..infinity) |
JacobiSC[z, (k)^2]-Divide[Pi,2*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Tan[\[Zeta]] == Divide[2*Pi,EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]]*Sum[Divide[(- 1)^(n)* (q)^(2*n)* Sin[2*n*\[Zeta]],1 + (q)^(2*n)], {n, 1, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.11.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk^{2}@{z}{k} = \frac{1}{k^{2}}\left(1-\frac{\compellintEk@@{k}}{K}\right)-\frac{2\pi^{2}}{k^{2}K^{2}}\sum_{n=1}^{\infty}\frac{nq^{n}}{1-q^{2n}}\cos@{2n\zeta}} | (JacobiSN(z, k))^(2) = (1)/((k)^(2))*(1 -(EllipticE(k))/(EllipticK(k)))-(2*(Pi)^(2))/((k)^(2)* (EllipticK(k))^(2))*sum((n*(q)^(n))/(1 - (q)^(2*n))*cos(2*n*zeta), n = 1..infinity) |
(JacobiSN[z, (k)^2])^(2) == Divide[1,(k)^(2)]*(1 -Divide[EllipticE[(k)^2],EllipticK[(k)^2]])-Divide[2*(Pi)^(2),(k)^(2)* (EllipticK[(k)^2])^(2)]*Sum[Divide[n*(q)^(n),1 - (q)^(2*n)]*Cos[2*n*\[Zeta]], {n, 1, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tau = i\ccompellintKk@{k}/\compellintKk@{k}} | tau = I*EllipticCK(k)/ EllipticK(k) |
\[Tau] == I*EllipticK[1-(k)^2]/ EllipticK[(k)^2] |
Failure | Failure | Error | Failed [30 / 30]
{Complex[0.8660254037844387, 0.49999999999999994] <- {Rule[k, 1], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.4867361401447923, 0.0147898206680519] <- {Rule[k, 2], Rule[τ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.12.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2Kk\Jacobiellsnk@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t-(n+\frac{1}{2})\tau)}}} | 2*K*k*JacobiSN(2*K*t, k) = sum((Pi)/(sin(Pi*(t -(n +(1)/(2))*tau))), n = - infinity..infinity) |
2*K*k*JacobiSN[2*K*t, (k)^2] == Sum[Divide[Pi,Sin[Pi*(t -(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t-(n+\frac{1}{2})\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m}}{t-m-(n+\frac{1}{2})\tau}\right)} | sum((Pi)/(sin(Pi*(t -(n +(1)/(2))*tau))), n = - infinity..infinity) = sum(sum(((- 1)^(m))/(t - m -(n +(1)/(2))* tau), m = - infinity..infinity), n = - infinity..infinity) |
Sum[Divide[Pi,Sin[Pi*(t -(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[(- 1)^(m),t - m -(n +Divide[1,2])* \[Tau]], {m, - Infinity, Infinity}, GenerateConditions->None], {n, - Infinity, Infinity}, GenerateConditions->None] |
Successful | Aborted | Skip - symbolical successful subtest | Skipped - Because timed out |
| 22.12.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2iKk\Jacobiellcnk@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t-(n+\frac{1}{2})\tau)}}} | 2*I*K*k*JacobiCN(2*K*t, k) = sum(((- 1)^(n)* Pi)/(sin(Pi*(t -(n +(1)/(2))*tau))), n = - infinity..infinity) |
2*I*K*k*JacobiCN[2*K*t, (k)^2] == Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t -(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t-(n+\frac{1}{2})\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m+n}}{t-m-(n+\frac{1}{2})\tau}\right)} | sum(((- 1)^(n)* Pi)/(sin(Pi*(t -(n +(1)/(2))*tau))), n = - infinity..infinity) = sum(sum(((- 1)^(m + n))/(t - m -(n +(1)/(2))* tau), m = - infinity..infinity), n = - infinity..infinity) |
Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t -(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[(- 1)^(m + n),t - m -(n +Divide[1,2])* \[Tau]], {m, - Infinity, Infinity}, GenerateConditions->None], {n, - Infinity, Infinity}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2iK\Jacobielldnk@{2Kt}{k} = \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan@{\pi(t-(n+\frac{1}{2})\tau)}}} | 2*I*EllipticK(k)*JacobiDN(2*K*t, k) = limit(sum((- 1)^(n)*(Pi)/(tan(Pi*(t -(n +(1)/(2))*tau))), n = - N..N), N = infinity) |
2*I*EllipticK[(k)^2]*JacobiDN[2*K*t, (k)^2] == Limit[Sum[(- 1)^(n)*Divide[Pi,Tan[Pi*(t -(n +Divide[1,2])*\[Tau])]], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan@{\pi(t-(n+\frac{1}{2})\tau)}} = \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\left(\lim_{M\to\infty}\sum_{m=-M}^{M}\frac{1}{t-m-(n+\frac{1}{2})\tau}\right)} | limit(sum((- 1)^(n)*(Pi)/(tan(Pi*(t -(n +(1)/(2))*tau))), n = - N..N), N = infinity) = limit(sum((- 1)^(n)*(limit(sum((1)/(t - m -(n +(1)/(2))* tau), m = - M..M), M = infinity)), n = - N..N), N = infinity) |
Limit[Sum[(- 1)^(n)*Divide[Pi,Tan[Pi*(t -(n +Divide[1,2])*\[Tau])]], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None] == Limit[Sum[(- 1)^(n)*(Limit[Sum[Divide[1,t - m -(n +Divide[1,2])* \[Tau]], {m, - M, M}, GenerateConditions->None], M -> Infinity, GenerateConditions->None]), {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2Kk\Jacobiellcdk@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t+\frac{1}{2}-(n+\frac{1}{2})\tau)}}} | 2*K*k*JacobiCD(2*K*t, k) = sum((Pi)/(sin(Pi*(t +(1)/(2)-(n +(1)/(2))*tau))), n = - infinity..infinity) |
2*K*k*JacobiCD[2*K*t, (k)^2] == Sum[Divide[Pi,Sin[Pi*(t +Divide[1,2]-(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t+\frac{1}{2}-(n+\frac{1}{2})\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m}}{t+\frac{1}{2}-m-(n+\frac{1}{2})\tau}\right)} | sum((Pi)/(sin(Pi*(t +(1)/(2)-(n +(1)/(2))*tau))), n = - infinity..infinity) = sum(sum(((- 1)^(m))/(t +(1)/(2)- m -(n +(1)/(2))* tau), m = - infinity..infinity), n = - infinity..infinity) |
Sum[Divide[Pi,Sin[Pi*(t +Divide[1,2]-(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[(- 1)^(m),t +Divide[1,2]- m -(n +Divide[1,2])* \[Tau]], {m, - Infinity, Infinity}, GenerateConditions->None], {n, - Infinity, Infinity}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -2iKkk^{\prime}\Jacobiellsdk@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t+\frac{1}{2}-(n+\frac{1}{2})\tau)}}} | - 2*I*K*k*sqrt(1 - (k)^(2))*JacobiSD(2*K*t, k) = sum(((- 1)^(n)* Pi)/(sin(Pi*(t +(1)/(2)-(n +(1)/(2))*tau))), n = - infinity..infinity) |
- 2*I*K*k*Sqrt[1 - (k)^(2)]*JacobiSD[2*K*t, (k)^2] == Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t +Divide[1,2]-(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t+\frac{1}{2}-(n+\frac{1}{2})\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m+n}}{t+\frac{1}{2}-m-(n+\frac{1}{2})\tau}\right)} | sum(((- 1)^(n)* Pi)/(sin(Pi*(t +(1)/(2)-(n +(1)/(2))*tau))), n = - infinity..infinity) = sum(sum(((- 1)^(m + n))/(t +(1)/(2)- m -(n +(1)/(2))* tau), m = - infinity..infinity), n = - infinity..infinity) |
Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t +Divide[1,2]-(n +Divide[1,2])*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[(- 1)^(m + n),t +Divide[1,2]- m -(n +Divide[1,2])* \[Tau]], {m, - Infinity, Infinity}, GenerateConditions->None], {n, - Infinity, Infinity}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2iKk^{\prime}\Jacobiellndk@{2Kt}{k} = \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan@{\pi(t+\frac{1}{2}-(n+\frac{1}{2})\tau)}}} | 2*I*EllipticK(k)*sqrt(1 - (k)^(2))*JacobiND(2*K*t, k) = limit(sum((- 1)^(n)*(Pi)/(tan(Pi*(t +(1)/(2)-(n +(1)/(2))*tau))), n = - N..N), N = infinity) |
2*I*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]*JacobiND[2*K*t, (k)^2] == Limit[Sum[(- 1)^(n)*Divide[Pi,Tan[Pi*(t +Divide[1,2]-(n +Divide[1,2])*\[Tau])]], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan@{\pi(t+\frac{1}{2}-(n+\frac{1}{2})\tau)}} = \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\lim_{M\to\infty}\left(\sum_{m=-M}^{M}\frac{1}{t+\frac{1}{2}-m-(n+\frac{1}{2})\tau}\right)} | limit(sum((- 1)^(n)*(Pi)/(tan(Pi*(t +(1)/(2)-(n +(1)/(2))*tau))), n = - N..N), N = infinity) = limit(sum((- 1)^(n)* limit(sum((1)/(t +(1)/(2)- m -(n +(1)/(2))* tau), m = - M..M), M = infinity), n = - N..N), N = infinity) |
Limit[Sum[(- 1)^(n)*Divide[Pi,Tan[Pi*(t +Divide[1,2]-(n +Divide[1,2])*\[Tau])]], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None] == Limit[Sum[(- 1)^(n)* Limit[Sum[Divide[1,t +Divide[1,2]- m -(n +Divide[1,2])* \[Tau]], {m, - M, M}, GenerateConditions->None], M -> Infinity, GenerateConditions->None], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2K\Jacobielldck@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t+\frac{1}{2}-n\tau)}}} | 2*EllipticK(k)*JacobiDC(2*K*t, k) = sum((Pi)/(sin(Pi*(t +(1)/(2)- n*tau))), n = - infinity..infinity) |
2*EllipticK[(k)^2]*JacobiDC[2*K*t, (k)^2] == Sum[Divide[Pi,Sin[Pi*(t +Divide[1,2]- n*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t+\frac{1}{2}-n\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m}}{t+\frac{1}{2}-m-n\tau}\right)} | sum((Pi)/(sin(Pi*(t +(1)/(2)- n*tau))), n = - infinity..infinity) = sum(sum(((- 1)^(m))/(t +(1)/(2)- m - n*tau), m = - infinity..infinity), n = - infinity..infinity) |
Sum[Divide[Pi,Sin[Pi*(t +Divide[1,2]- n*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[(- 1)^(m),t +Divide[1,2]- m - n*\[Tau]], {m, - Infinity, Infinity}, GenerateConditions->None], {n, - Infinity, Infinity}, GenerateConditions->None] |
Successful | Aborted | Skip - symbolical successful subtest | Skipped - Because timed out |
| 22.12.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2Kk^{\prime}\Jacobiellnck@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t+\frac{1}{2}-n\tau)}}} | 2*EllipticK(k)*sqrt(1 - (k)^(2))*JacobiNC(2*K*t, k) = sum(((- 1)^(n)* Pi)/(sin(Pi*(t +(1)/(2)- n*tau))), n = - infinity..infinity) |
2*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]*JacobiNC[2*K*t, (k)^2] == Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t +Divide[1,2]- n*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t+\frac{1}{2}-n\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m+n}}{t+\frac{1}{2}-m-n\tau}\right)} | sum(((- 1)^(n)* Pi)/(sin(Pi*(t +(1)/(2)- n*tau))), n = - infinity..infinity) = sum(sum(((- 1)^(m + n))/(t +(1)/(2)- m - n*tau), m = - infinity..infinity), n = - infinity..infinity) |
Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t +Divide[1,2]- n*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[(- 1)^(m + n),t +Divide[1,2]- m - n*\[Tau]], {m, - Infinity, Infinity}, GenerateConditions->None], {n, - Infinity, Infinity}, GenerateConditions->None] |
Successful | Aborted | Skip - symbolical successful subtest | Skipped - Because timed out |
| 22.12.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -2Kk^{\prime}\Jacobiellsck@{2Kt}{k} = \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan@{\pi(t+\frac{1}{2}-n\tau)}}} | - 2*EllipticK(k)*sqrt(1 - (k)^(2))*JacobiSC(2*K*t, k) = limit(sum((- 1)^(n)*(Pi)/(tan(Pi*(t +(1)/(2)- n*tau))), n = - N..N), N = infinity) |
- 2*EllipticK[(k)^2]*Sqrt[1 - (k)^(2)]*JacobiSC[2*K*t, (k)^2] == Limit[Sum[(- 1)^(n)*Divide[Pi,Tan[Pi*(t +Divide[1,2]- n*\[Tau])]], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan@{\pi(t+\frac{1}{2}-n\tau)}} = \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\left(\lim_{M\to\infty}\sum_{m=-M}^{M}\frac{1}{t+\frac{1}{2}-m-n\tau}\right)} | limit(sum((- 1)^(n)*(Pi)/(tan(Pi*(t +(1)/(2)- n*tau))), n = - N..N), N = infinity) = limit(sum((- 1)^(n)*(limit(sum((1)/(t +(1)/(2)- m - n*tau), m = - M..M), M = infinity)), n = - N..N), N = infinity) |
Limit[Sum[(- 1)^(n)*Divide[Pi,Tan[Pi*(t +Divide[1,2]- n*\[Tau])]], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None] == Limit[Sum[(- 1)^(n)*(Limit[Sum[Divide[1,t +Divide[1,2]- m - n*\[Tau]], {m, - M, M}, GenerateConditions->None], M -> Infinity, GenerateConditions->None]), {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2K\Jacobiellnsk@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t-n\tau)}}} | 2*EllipticK(k)*JacobiNS(2*K*t, k) = sum((Pi)/(sin(Pi*(t - n*tau))), n = - infinity..infinity) |
2*EllipticK[(k)^2]*JacobiNS[2*K*t, (k)^2] == Sum[Divide[Pi,Sin[Pi*(t - n*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}\frac{\pi}{\sin@{\pi(t-n\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m}}{t-m-n\tau}\right)} | sum((Pi)/(sin(Pi*(t - n*tau))), n = - infinity..infinity) = sum(sum(((- 1)^(m))/(t - m - n*tau), m = - infinity..infinity), n = - infinity..infinity) |
Sum[Divide[Pi,Sin[Pi*(t - n*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[(- 1)^(m),t - m - n*\[Tau]], {m, - Infinity, Infinity}, GenerateConditions->None], {n, - Infinity, Infinity}, GenerateConditions->None] |
Successful | Aborted | Skip - symbolical successful subtest | Skipped - Because timed out |
| 22.12.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2K\Jacobielldsk@{2Kt}{k} = \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t-n\tau)}}} | 2*EllipticK(k)*JacobiDS(2*K*t, k) = sum(((- 1)^(n)* Pi)/(sin(Pi*(t - n*tau))), n = - infinity..infinity) |
2*EllipticK[(k)^2]*JacobiDS[2*K*t, (k)^2] == Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t - n*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}\frac{(-1)^{n}\pi}{\sin@{\pi(t-n\tau)}} = \sum_{n=-\infty}^{\infty}\left(\sum_{m=-\infty}^{\infty}\frac{(-1)^{m+n}}{t-m-n\tau}\right)} | sum(((- 1)^(n)* Pi)/(sin(Pi*(t - n*tau))), n = - infinity..infinity) = sum(sum(((- 1)^(m + n))/(t - m - n*tau), m = - infinity..infinity), n = - infinity..infinity) |
Sum[Divide[(- 1)^(n)* Pi,Sin[Pi*(t - n*\[Tau])]], {n, - Infinity, Infinity}, GenerateConditions->None] == Sum[Sum[Divide[(- 1)^(m + n),t - m - n*\[Tau]], {m, - Infinity, Infinity}, GenerateConditions->None], {n, - Infinity, Infinity}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2K\Jacobiellcsk@{2Kt}{k} = \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan@{\pi(t-n\tau)}}} | 2*EllipticK(k)*JacobiCS(2*K*t, k) = limit(sum((- 1)^(n)*(Pi)/(tan(Pi*(t - n*tau))), n = - N..N), N = infinity) |
2*EllipticK[(k)^2]*JacobiCS[2*K*t, (k)^2] == Limit[Sum[(- 1)^(n)*Divide[Pi,Tan[Pi*(t - n*\[Tau])]], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.12.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\frac{\pi}{\tan@{\pi(t-n\tau)}} = \lim_{N\to\infty}\sum_{n=-N}^{N}(-1)^{n}\left(\lim_{M\to\infty}\sum_{m=-M}^{M}\frac{1}{t-m-n\tau}\right)} | limit(sum((- 1)^(n)*(Pi)/(tan(Pi*(t - n*tau))), n = - N..N), N = infinity) = limit(sum((- 1)^(n)*(limit(sum((1)/(t - m - n*tau), m = - M..M), M = infinity)), n = - N..N), N = infinity) |
Limit[Sum[(- 1)^(n)*Divide[Pi,Tan[Pi*(t - n*\[Tau])]], {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None] == Limit[Sum[(- 1)^(n)*(Limit[Sum[Divide[1,t - m - n*\[Tau]], {m, - M, M}, GenerateConditions->None], M -> Infinity, GenerateConditions->None]), {n, - N, N}, GenerateConditions->None], N -> Infinity, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.13.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellsnk@{z}{k}\right)^{2} = \left(1-\Jacobiellsnk^{2}@{z}{k}\right)\left(1-k^{2}\Jacobiellsnk^{2}@{z}{k}\right)} | (diff(JacobiSN(z, k), z))^(2) = (1 - (JacobiSN(z, k))^(2))*(1 - (k)^(2)* (JacobiSN(z, k))^(2)) |
(D[JacobiSN[z, (k)^2], z])^(2) == (1 - (JacobiSN[z, (k)^2])^(2))*(1 - (k)^(2)* (JacobiSN[z, (k)^2])^(2)) |
Successful | Successful | - | Successful [Tested: 21] |
| 22.13.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellcnk@{z}{k}\right)^{2} = {\left(1-\Jacobiellcnk^{2}@{z}{k}\right)}{\left({k^{\prime}}^{2}+k^{2}\Jacobiellcnk^{2}@{z}{k}\right)}} | (diff(JacobiCN(z, k), z))^(2) = (1 - (JacobiCN(z, k))^(2))*(1 - (k)^(2)+ (k)^(2)* (JacobiCN(z, k))^(2)) |
(D[JacobiCN[z, (k)^2], z])^(2) == (1 - (JacobiCN[z, (k)^2])^(2))*(1 - (k)^(2)+ (k)^(2)* (JacobiCN[z, (k)^2])^(2)) |
Successful | Successful | - | Successful [Tested: 21] |
| 22.13.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobielldnk@{z}{k}\right)^{2} = \left(1-\Jacobielldnk^{2}@{z}{k}\right)\left(\Jacobielldnk^{2}@{z}{k}-{k^{\prime}}^{2}\right)} | (diff(JacobiDN(z, k), z))^(2) = (1 - (JacobiDN(z, k))^(2))*((JacobiDN(z, k))^(2)-1 - (k)^(2)) |
(D[JacobiDN[z, (k)^2], z])^(2) == (1 - (JacobiDN[z, (k)^2])^(2))*((JacobiDN[z, (k)^2])^(2)-1 - (k)^(2)) |
Failure | Failure | Failed [21 / 21] 21/21]: [[1.137161176+.7719908960*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}14.77981366-.6810923425*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[1.1371611759337996, 0.7719908961474706] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[14.779813656775712, -0.6810923360985438] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.13.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellcdk@{z}{k}\right)^{2} = \left(1-\Jacobiellcdk^{2}@{z}{k}\right)\left(1-k^{2}\Jacobiellcdk^{2}@{z}{k}\right)} | (diff(JacobiCD(z, k), z))^(2) = (1 - (JacobiCD(z, k))^(2))*(1 - (k)^(2)* (JacobiCD(z, k))^(2)) |
(D[JacobiCD[z, (k)^2], z])^(2) == (1 - (JacobiCD[z, (k)^2])^(2))*(1 - (k)^(2)* (JacobiCD[z, (k)^2])^(2)) |
Successful | Successful | - | Successful [Tested: 21] |
| 22.13.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellsdk@{z}{k}\right)^{2} = {\left(1-{k^{\prime}}^{2}\Jacobiellsdk^{2}@{z}{k}\right)}{\left(1+k^{2}\Jacobiellsdk^{2}@{z}{k}\right)}} | (diff(JacobiSD(z, k), z))^(2) = (1 -1 - (k)^(2)*(JacobiSD(z, k))^(2))*(1 + (k)^(2)* (JacobiSD(z, k))^(2)) |
(D[JacobiSD[z, (k)^2], z])^(2) == (1 -1 - (k)^(2)*(JacobiSD[z, (k)^2])^(2))*(1 + (k)^(2)* (JacobiSD[z, (k)^2])^(2)) |
Failure | Failure | Failed [21 / 21] 21/21]: [[.3306277626+2.965675443*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}3.240181814+.5678364413*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[0.33062776288262774, 2.9656754410633357] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[3.24018181473062, 0.5678364360004244] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.13.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellndk@{z}{k}\right)^{2} = \left(\Jacobiellndk^{2}@{z}{k}-1\right)\left(1-{k^{\prime}}^{2}\Jacobiellndk^{2}@{z}{k}\right)} | (diff(JacobiND(z, k), z))^(2) = ((JacobiND(z, k))^(2)- 1)*(1 -1 - (k)^(2)*(JacobiND(z, k))^(2)) |
(D[JacobiND[z, (k)^2], z])^(2) == ((JacobiND[z, (k)^2])^(2)- 1)*(1 -1 - (k)^(2)*(JacobiND[z, (k)^2])^(2)) |
Failure | Failure | Failed [21 / 21] 21/21]: [[-.6693722376+2.965675443*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}15.46527968+2.623409101*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[-0.6693722371173725, 2.965675441063337] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[15.465279679493392, 2.6234090772942062] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.13.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobielldck@{z}{k}\right)^{2} = \left(\Jacobielldck^{2}@{z}{k}-1\right)\left(\Jacobielldck^{2}@{z}{k}-k^{2}\right)} | (diff(JacobiDC(z, k), z))^(2) = ((JacobiDC(z, k))^(2)- 1)*((JacobiDC(z, k))^(2)- (k)^(2)) |
(D[JacobiDC[z, (k)^2], z])^(2) == ((JacobiDC[z, (k)^2])^(2)- 1)*((JacobiDC[z, (k)^2])^(2)- (k)^(2)) |
Successful | Successful | - | Successful [Tested: 21] |
| 22.13.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellnck@{z}{k}\right)^{2} = {\left(k^{2}+{k^{\prime}}^{2}\Jacobiellnck^{2}@{z}{k}\right)}{\left(\Jacobiellnck^{2}@{z}{k}-1\right)}} | (diff(JacobiNC(z, k), z))^(2) = ((k)^(2)+1 - (k)^(2)*(JacobiNC(z, k))^(2))*((JacobiNC(z, k))^(2)- 1) |
(D[JacobiNC[z, (k)^2], z])^(2) == ((k)^(2)+1 - (k)^(2)*(JacobiNC[z, (k)^2])^(2))*((JacobiNC[z, (k)^2])^(2)- 1) |
Failure | Failure | Failed [20 / 21] 20/21]: [[-1.244125150+.6620171546*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}.726292651-.1255426739*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [20 / 21]
{Complex[-1.2441251486756877, 0.66201715389323] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.726292650669289, -0.12554267275387493] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.13.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellsck@{z}{k}\right)^{2} = \left(1+\Jacobiellsck^{2}@{z}{k}\right)\left(1+{k^{\prime}}^{2}\Jacobiellsck^{2}@{z}{k}\right)} | (diff(JacobiSC(z, k), z))^(2) = (1 + (JacobiSC(z, k))^(2))*(1 +1 - (k)^(2)*(JacobiSC(z, k))^(2)) |
(D[JacobiSC[z, (k)^2], z])^(2) == (1 + (JacobiSC[z, (k)^2])^(2))*(1 +1 - (k)^(2)*(JacobiSC[z, (k)^2])^(2)) |
Failure | Failure | Failed [21 / 21] 21/21]: [[-2.244125150+.6620171546*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}-.273707349-.1255426740*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[-2.244125148675687, 0.6620171538932291] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.27370734933071006, -0.12554267275387854] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.13.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellnsk@{z}{k}\right)^{2} = \left(\Jacobiellnsk^{2}@{z}{k}-k^{2}\right)\left(\Jacobiellnsk^{2}@{z}{k}-1\right)} | (diff(JacobiNS(z, k), z))^(2) = ((JacobiNS(z, k))^(2)- (k)^(2))*((JacobiNS(z, k))^(2)- 1) |
(D[JacobiNS[z, (k)^2], z])^(2) == ((JacobiNS[z, (k)^2])^(2)- (k)^(2))*((JacobiNS[z, (k)^2])^(2)- 1) |
Successful | Successful | - | Successful [Tested: 21] |
| 22.13.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobielldsk@{z}{k}\right)^{2} = \left(\Jacobielldsk^{2}@{z}{k}-{k^{\prime}}^{2}\right)\left(k^{2}+\Jacobielldsk^{2}@{z}{k}\right)} | (diff(JacobiDS(z, k), z))^(2) = ((JacobiDS(z, k))^(2)-1 - (k)^(2))*((k)^(2)+ (JacobiDS(z, k))^(2)) |
(D[JacobiDS[z, (k)^2], z])^(2) == ((JacobiDS[z, (k)^2])^(2)-1 - (k)^(2))*((k)^(2)+ (JacobiDS[z, (k)^2])^(2)) |
Failure | Failure | Failed [21 / 21] 21/21]: [[2.407829919-1.634616811*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}17.28421715+.7965017848*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[2.4078299188565357, -1.6346168126100018] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[17.284217154319762, 0.7965017768592271] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.13.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\deriv{}{z}\Jacobiellcsk@{z}{k}\right)^{2} = \left(1+\Jacobiellcsk^{2}@{z}{k}\right)\left({k^{\prime}}^{2}+\Jacobiellcsk^{2}@{z}{k}\right)} | (diff(JacobiCS(z, k), z))^(2) = (1 + (JacobiCS(z, k))^(2))*(1 - (k)^(2)+ (JacobiCS(z, k))^(2)) |
(D[JacobiCS[z, (k)^2], z])^(2) == (1 + (JacobiCS[z, (k)^2])^(2))*(1 - (k)^(2)+ (JacobiCS[z, (k)^2])^(2)) |
Successful | Successful | - | Successful [Tested: 21] |
| 22.13.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellsnk@{z}{k} = -(1+k^{2})\Jacobiellsnk@{z}{k}+2k^{2}\Jacobiellsnk^{3}@{z}{k}} | diff(JacobiSN(z, k), [z$(2)]) = -(1 + (k)^(2))* JacobiSN(z, k)+ 2*(k)^(2)* (JacobiSN(z, k))^(3) |
D[JacobiSN[z, (k)^2], {z, 2}] == -(1 + (k)^(2))* JacobiSN[z, (k)^2]+ 2*(k)^(2)* (JacobiSN[z, (k)^2])^(3) |
Successful | Successful | - | Successful [Tested: 21] |
| 22.13.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellcnk@{z}{k} = -({k^{\prime}}^{2}-k^{2})\Jacobiellcnk@{z}{k}-2k^{2}\Jacobiellcnk^{3}@{z}{k}} | diff(JacobiCN(z, k), [z$(2)]) = -(1 - (k)^(2)- (k)^(2))* JacobiCN(z, k)- 2*(k)^(2)* (JacobiCN(z, k))^(3) |
D[JacobiCN[z, (k)^2], {z, 2}] == -(1 - (k)^(2)- (k)^(2))* JacobiCN[z, (k)^2]- 2*(k)^(2)* (JacobiCN[z, (k)^2])^(3) |
Successful | Successful | - | Successful [Tested: 21] |
| 22.13.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobielldnk@{z}{k} = (1+{k^{\prime}}^{2})\Jacobielldnk@{z}{k}-2\Jacobielldnk^{3}@{z}{k}} | diff(JacobiDN(z, k), [z$(2)]) = (1 +1 - (k)^(2))* JacobiDN(z, k)- 2*(JacobiDN(z, k))^(3) |
D[JacobiDN[z, (k)^2], {z, 2}] == (1 +1 - (k)^(2))* JacobiDN[z, (k)^2]- 2*(JacobiDN[z, (k)^2])^(3) |
Successful | Successful | - | Successful [Tested: 21] |
| 22.13.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellcdk@{z}{k} = -(1+k^{2})\Jacobiellcdk@{z}{k}+2k^{2}\Jacobiellcdk^{3}@{z}{k}} | diff(JacobiCD(z, k), [z$(2)]) = -(1 + (k)^(2))* JacobiCD(z, k)+ 2*(k)^(2)* (JacobiCD(z, k))^(3) |
D[JacobiCD[z, (k)^2], {z, 2}] == -(1 + (k)^(2))* JacobiCD[z, (k)^2]+ 2*(k)^(2)* (JacobiCD[z, (k)^2])^(3) |
Successful | Successful | - | Successful [Tested: 21] |
| 22.13.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellsdk@{z}{k} = (k^{2}-{k^{\prime}}^{2})\Jacobiellsdk@{z}{k}-2k^{2}{k^{\prime}}^{2}\Jacobiellsdk^{3}@{z}{k}} | diff(JacobiSD(z, k), [z$(2)]) = ((k)^(2)-1 - (k)^(2))* JacobiSD(z, k)- 2*(k)^(2)*1 - (k)^(2)*(JacobiSD(z, k))^(3) |
D[JacobiSD[z, (k)^2], {z, 2}] == ((k)^(2)-1 - (k)^(2))* JacobiSD[z, (k)^2]- 2*(k)^(2)*1 - (k)^(2)*(JacobiSD[z, (k)^2])^(3) |
Failure | Failure | Failed [21 / 21] 21/21]: [[3.191457484+2.523217914*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}8.747979617-5.269762671*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[3.1914574835245033, 2.523217912470552] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[8.747979609525483, -5.269762670615425] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.13.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellndk@{z}{k} = (1+{k^{\prime}}^{2})\Jacobiellndk@{z}{k}-2{k^{\prime}}^{2}\Jacobiellndk^{3}@{z}{k}} | diff(JacobiND(z, k), [z$(2)]) = (1 +1 - (k)^(2))* JacobiND(z, k)- 2*1 - (k)^(2)*(JacobiND(z, k))^(3) |
D[JacobiND[z, (k)^2], {z, 2}] == (1 +1 - (k)^(2))* JacobiND[z, (k)^2]- 2*1 - (k)^(2)*(JacobiND[z, (k)^2])^(3) |
Failure | Failure | Failed [21 / 21] 21/21]: [[3.040301731+2.018052700*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}3.903394000-12.57828103*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[3.0403017307041966, 2.01805269920667] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[3.903393981406644, -12.578281030301023] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.13.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobielldck@{z}{k} = -(1+k^{2})\Jacobielldck@{z}{k}+2\Jacobielldck^{3}@{z}{k}} | diff(JacobiDC(z, k), [z$(2)]) = -(1 + (k)^(2))* JacobiDC(z, k)+ 2*(JacobiDC(z, k))^(3) |
D[JacobiDC[z, (k)^2], {z, 2}] == -(1 + (k)^(2))* JacobiDC[z, (k)^2]+ 2*(JacobiDC[z, (k)^2])^(3) |
Successful | Successful | - | Successful [Tested: 21] |
| 22.13.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellnck@{z}{k} = (k^{2}-{k^{\prime}}^{2})\Jacobiellnck@{z}{k}+2{k^{\prime}}^{2}\Jacobiellnck^{3}@{z}{k}} | diff(JacobiNC(z, k), [z$(2)]) = ((k)^(2)-1 - (k)^(2))* JacobiNC(z, k)+ 2*1 - (k)^(2)*(JacobiNC(z, k))^(3) |
D[JacobiNC[z, (k)^2], {z, 2}] == ((k)^(2)-1 - (k)^(2))* JacobiNC[z, (k)^2]+ 2*1 - (k)^(2)*(JacobiNC[z, (k)^2])^(3) |
Failure | Failure | Failed [21 / 21] 21/21]: [[1.495832765+2.956203453*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}3.847566639+.844372345e-1*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[1.4958327644324174, 2.9562034517436775] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[3.8475666387741003, 0.08443723368166078] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.13.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellsck@{z}{k} = (1+{k^{\prime}}^{2})\Jacobiellsck@{z}{k}+2{k^{\prime}}^{2}\Jacobiellsck^{3}@{z}{k}} | diff(JacobiSC(z, k), [z$(2)]) = (1 +1 - (k)^(2))* JacobiSC(z, k)+ 2*1 - (k)^(2)*(JacobiSC(z, k))^(3) |
D[JacobiSC[z, (k)^2], {z, 2}] == (1 +1 - (k)^(2))* JacobiSC[z, (k)^2]+ 2*1 - (k)^(2)*(JacobiSC[z, (k)^2])^(3) |
Failure | Failure | Failed [21 / 21] 21/21]: [[-2.525815950+1.181755196*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}-3.577866152+.2036740201*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[-2.5258159501097865, 1.1817551948561285] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-3.5778661524913966, 0.20367401847233424] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.13.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellnsk@{z}{k} = -(1+k^{2})\Jacobiellnsk@{z}{k}+2\Jacobiellnsk^{3}@{z}{k}} | diff(JacobiNS(z, k), [z$(2)]) = -(1 + (k)^(2))* JacobiNS(z, k)+ 2*(JacobiNS(z, k))^(3) |
D[JacobiNS[z, (k)^2], {z, 2}] == -(1 + (k)^(2))* JacobiNS[z, (k)^2]+ 2*(JacobiNS[z, (k)^2])^(3) |
Successful | Successful | - | Successful [Tested: 21] |
| 22.13.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobielldsk@{z}{k} = (k^{2}-{k^{\prime}}^{2})\Jacobielldsk@{z}{k}+2\Jacobielldsk^{3}@{z}{k}} | diff(JacobiDS(z, k), [z$(2)]) = ((k)^(2)-1 - (k)^(2))* JacobiDS(z, k)+ 2*(JacobiDS(z, k))^(3) |
D[JacobiDS[z, (k)^2], {z, 2}] == ((k)^(2)-1 - (k)^(2))* JacobiDS[z, (k)^2]+ 2*(JacobiDS[z, (k)^2])^(3) |
Failure | Failure | Failed [21 / 21] 21/21]: [[1.446566498-1.129997698*I <- {z = 1/2*3^(1/2)+1/2*I, k = 1}-.2935291263-10.85414309*I <- {z = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [21 / 21]
{Complex[1.4465664983977982, -1.1299976975966786] <- {Rule[k, 1], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.293529123621927, -10.854143085101464] <- {Rule[k, 2], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.13.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{}{z}\Jacobiellcsk@{z}{k} = (1+{k^{\prime}}^{2})\Jacobiellcsk@{z}{k}+2\Jacobiellcsk^{3}@{z}{k}} | diff(JacobiCS(z, k), [z$(2)]) = (1 +1 - (k)^(2))* JacobiCS(z, k)+ 2*(JacobiCS(z, k))^(3) |
D[JacobiCS[z, (k)^2], {z, 2}] == (1 +1 - (k)^(2))* JacobiCS[z, (k)^2]+ 2*(JacobiCS[z, (k)^2])^(3) |
Successful | Successful | - | Successful [Tested: 21] |
| 22.14.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellsnk@{x}{k}\diff{x} = k^{-1}\ln@{\Jacobielldnk@{x}{k}-k\Jacobiellcnk@{x}{k}}} | int(JacobiSN(x, k), x) = (k)^(- 1)* ln(JacobiDN(x, k)- k*JacobiCN(x, k)) |
Integrate[JacobiSN[x, (k)^2], x, GenerateConditions->None] == (k)^(- 1)* Log[JacobiDN[x, (k)^2]- k*JacobiCN[x, (k)^2]] |
Successful | Failure | - | Failed [3 / 9]
{Indeterminate <- {Rule[k, 1], Rule[x, 1.5]}Indeterminate <- {Rule[k, 1], Rule[x, 0.5]} |
| 22.14.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellcnk@{x}{k}\diff{x} = k^{-1}\Acos@{\Jacobielldnk@{x}{k}}} | Error |
Integrate[JacobiCN[x, (k)^2], x, GenerateConditions->None] == (k)^(- 1)* ArcCos[JacobiDN[x, (k)^2]] |
Missing Macro Error | Failure | - | Failed [3 / 9]
{-1.2690416691147375 <- {Rule[k, 3], Rule[x, 1.5]}-2.5226182800392123 <- {Rule[k, 2], Rule[x, 2]} |
| 22.14.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobielldnk@{x}{k}\diff{x} = \Asin@{\Jacobiellsnk@{x}{k}}} | Error |
Integrate[JacobiDN[x, (k)^2], x, GenerateConditions->None] == ArcSin[JacobiSN[x, (k)^2]] |
Missing Macro Error | Failure | - | Failed [3 / 9]
{6.283185307179586 <- {Rule[k, 3], Rule[x, 1.5]}6.283185307179586 <- {Rule[k, 2], Rule[x, 2]} |
| 22.14.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Asin@{\Jacobiellsnk@{x}{k}} = \Jacobiamk@{x}{k}} | Error |
ArcSin[JacobiSN[x, (k)^2]] == JacobiAmplitude[x, Power[k, 2]] |
Missing Macro Error | Failure | - | Failed [1 / 3]
{-6.283185307179586 <- {Rule[k, 3], Rule[x, Rational[3, 2]]} |
| 22.14.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellcdk@{x}{k}\diff{x} = k^{-1}\ln@{\Jacobiellndk@{x}{k}+k\Jacobiellsdk@{x}{k}}} | int(JacobiCD(x, k), x) = (k)^(- 1)* ln(JacobiND(x, k)+ k*JacobiSD(x, k)) |
Integrate[JacobiCD[x, (k)^2], x, GenerateConditions->None] == (k)^(- 1)* Log[JacobiND[x, (k)^2]+ k*JacobiSD[x, (k)^2]] |
Successful | Failure | - | Successful [Tested: 9] |
| 22.14.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellsdk@{x}{k}\diff{x} = (kk^{\prime})^{-1}\Asin@{-k\Jacobiellcdk@{x}{k}}} | Error |
Integrate[JacobiSD[x, (k)^2], x, GenerateConditions->None] == (k*Sqrt[1 - (k)^(2)])^(- 1)* ArcSin[- k*JacobiCD[x, (k)^2]] |
Missing Macro Error | Aborted | - | Failed [6 / 9]
{Indeterminate <- {Rule[k, 1], Rule[x, 1.5]}Complex[0.7955664885698261, 0.9068996821171089] <- {Rule[k, 2], Rule[x, 1.5]} |
| 22.14.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellndk@{x}{k}\diff{x} = {k^{\prime}}^{-1}\Acos@{\Jacobiellcdk@{x}{k}}} | Error |
Integrate[JacobiND[x, (k)^2], x, GenerateConditions->None] == (Sqrt[1 - (k)^(2)])^(- 1)* ArcCos[JacobiCD[x, (k)^2]] |
Missing Macro Error | Failure | - | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]}Plus[Complex[0.0, -1.7320508075688772], Times[-0.3333333333333333, ArcCos[JacobiCD[x, 4.0]], Power[Plus[1.0, Times[-1.0, Power[JacobiCD[x, 4.0], 2]]], Rational[1, 2]], JacobiDN[x, 4.0], Power[JacobiSN[x, 4.0], -1]]] <- {Rule[k, 2]} |
| 22.14.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobielldck@{x}{k}\diff{x} = \ln@{\Jacobiellnck@{x}{k}+\Jacobiellsck@{x}{k}}} | int(JacobiDC(x, k), x) = ln(JacobiNC(x, k)+ JacobiSC(x, k)) |
Integrate[JacobiDC[x, (k)^2], x, GenerateConditions->None] == Log[JacobiNC[x, (k)^2]+ JacobiSC[x, (k)^2]] |
Successful | Successful | - | Successful [Tested: 9] |
| 22.14.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellnck@{x}{k}\diff{x} = {k^{\prime}}^{-1}\ln@{\Jacobielldck@{x}{k}+k^{\prime}\Jacobiellsck@{x}{k}}} | int(JacobiNC(x, k), x) = (sqrt(1 - (k)^(2)))^(- 1)* ln(JacobiDC(x, k)+sqrt(1 - (k)^(2))*JacobiSC(x, k)) |
Integrate[JacobiNC[x, (k)^2], x, GenerateConditions->None] == (Sqrt[1 - (k)^(2)])^(- 1)* Log[JacobiDC[x, (k)^2]+Sqrt[1 - (k)^(2)]*JacobiSC[x, (k)^2]] |
Successful | Successful | - | Successful [Tested: 9] |
| 22.14.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellsck@{x}{k}\diff{x} = {k^{\prime}}^{-1}\ln@{\Jacobielldck@{x}{k}+k^{\prime}\Jacobiellnck@{x}{k}}} | int(JacobiSC(x, k), x) = (sqrt(1 - (k)^(2)))^(- 1)* ln(JacobiDC(x, k)+sqrt(1 - (k)^(2))*JacobiNC(x, k)) |
Integrate[JacobiSC[x, (k)^2], x, GenerateConditions->None] == (Sqrt[1 - (k)^(2)])^(- 1)* Log[JacobiDC[x, (k)^2]+Sqrt[1 - (k)^(2)]*JacobiNC[x, (k)^2]] |
Successful | Successful | - | Successful [Tested: 9] |
| 22.14.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellnsk@{x}{k}\diff{x} = \ln@{\Jacobielldsk@{x}{k}-\Jacobiellcsk@{x}{k}}} | int(JacobiNS(x, k), x) = ln(JacobiDS(x, k)- JacobiCS(x, k)) |
Integrate[JacobiNS[x, (k)^2], x, GenerateConditions->None] == Log[JacobiDS[x, (k)^2]- JacobiCS[x, (k)^2]] |
Successful | Successful | - | Successful [Tested: 9] |
| 22.14.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobielldsk@{x}{k}\diff{x} = \ln@{\Jacobiellnsk@{x}{k}-\Jacobiellcsk@{x}{k}}} | int(JacobiDS(x, k), x) = ln(JacobiNS(x, k)- JacobiCS(x, k)) |
Integrate[JacobiDS[x, (k)^2], x, GenerateConditions->None] == Log[JacobiNS[x, (k)^2]- JacobiCS[x, (k)^2]] |
Successful | Successful | - | Successful [Tested: 9] |
| 22.14.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\Jacobiellcsk@{x}{k}\diff{x} = \ln@{\Jacobiellnsk@{x}{k}-\Jacobielldsk@{x}{k}}} | int(JacobiCS(x, k), x) = ln(JacobiNS(x, k)- JacobiDS(x, k)) |
Integrate[JacobiCS[x, (k)^2], x, GenerateConditions->None] == Log[JacobiNS[x, (k)^2]- JacobiDS[x, (k)^2]] |
Successful | Successful | - | Successful [Tested: 9] |
| 22.14.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\frac{\diff{x}}{\Jacobiellsnk@{x}{k}} = \ln@{\frac{\Jacobiellsnk@{x}{k}}{\Jacobiellcnk@{x}{k}+\Jacobielldnk@{x}{k}}}} | int((1)/(JacobiSN(x, k)), x) = ln((JacobiSN(x, k))/(JacobiCN(x, k)+ JacobiDN(x, k))) |
Integrate[Divide[1,JacobiSN[x, (k)^2]], x, GenerateConditions->None] == Log[Divide[JacobiSN[x, (k)^2],JacobiCN[x, (k)^2]+ JacobiDN[x, (k)^2]]] |
Successful | Successful | - | Successful [Tested: 9] |
| 22.14.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\frac{\Jacobiellcnk@{x}{k}\diff{x}}{\Jacobiellsnk@{x}{k}} = \frac{1}{2}\ln@{\frac{1-\Jacobielldnk@{x}{k}}{1+\Jacobielldnk@{x}{k}}}} | int((JacobiCN(x, k))/(JacobiSN(x, k)), x) = (1)/(2)*ln((1 - JacobiDN(x, k))/(1 + JacobiDN(x, k))) |
Integrate[Divide[JacobiCN[x, (k)^2],JacobiSN[x, (k)^2]], x, GenerateConditions->None] == Divide[1,2]*Log[Divide[1 - JacobiDN[x, (k)^2],1 + JacobiDN[x, (k)^2]]] |
Failure | Failure | Successful [Tested: 9] | Failed [6 / 9]
{0.6931471805599452 <- {Rule[k, 2], Rule[x, 1.5]}Complex[1.0986122886681102, 3.141592653589793] <- {Rule[k, 3], Rule[x, 1.5]} |
| 22.14.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int\frac{\Jacobiellcnk@{x}{k}\diff{x}}{\Jacobiellsnk^{2}@{x}{k}} = -\frac{\Jacobielldnk@{x}{k}}{\Jacobiellsnk@{x}{k}}} | int((JacobiCN(x, k))/((JacobiSN(x, k))^(2)), x) = -(JacobiDN(x, k))/(JacobiSN(x, k)) |
Integrate[Divide[JacobiCN[x, (k)^2],(JacobiSN[x, (k)^2])^(2)], x, GenerateConditions->None] == -Divide[JacobiDN[x, (k)^2],JacobiSN[x, (k)^2]] |
Successful | Successful | - | Successful [Tested: 9] |
| 22.14.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\compellintKk@{k}}\ln@{\Jacobiellsnk@{t}{k}}\diff{t} = -\tfrac{\cpi}{4}\ccompellintKk@{k}-\tfrac{1}{2}\compellintKk@{k}\ln@@{k}} | int(ln(JacobiSN(t, k)), t = 0..EllipticK(k)) = -(Pi)/(4)*EllipticCK(k)-(1)/(2)*EllipticK(k)*ln(k) |
Integrate[Log[JacobiSN[t, (k)^2]], {t, 0, EllipticK[(k)^2]}, GenerateConditions->None] == -Divide[Pi,4]*EllipticK[1-(k)^2]-Divide[1,2]*EllipticK[(k)^2]*Log[k] |
Failure | Failure | Error | Skipped - Because timed out |
| 22.14.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\compellintKk@{k}}\ln@{\Jacobiellcnk@{t}{k}}\diff{t} = -\tfrac{\cpi}{4}\ccompellintKk@{k}+\tfrac{1}{2}\compellintKk@{k}\ln@{k^{\prime}/k}} | int(ln(JacobiCN(t, k)), t = 0..EllipticK(k)) = -(Pi)/(4)*EllipticCK(k)+(1)/(2)*EllipticK(k)*ln(sqrt(1 - (k)^(2))/ k) |
Integrate[Log[JacobiCN[t, (k)^2]], {t, 0, EllipticK[(k)^2]}, GenerateConditions->None] == -Divide[Pi,4]*EllipticK[1-(k)^2]+Divide[1,2]*EllipticK[(k)^2]*Log[Sqrt[1 - (k)^(2)]/ k] |
Failure | Failure | Error | Skipped - Because timed out |
| 22.14.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\compellintKk@{k}}\ln@{\Jacobielldnk@{t}{k}}\diff{t} = \tfrac{1}{2}\compellintKk@{k}\ln@@{k^{\prime}}} | int(ln(JacobiDN(t, k)), t = 0..EllipticK(k)) = (1)/(2)*EllipticK(k)*ln(sqrt(1 - (k)^(2))) |
Integrate[Log[JacobiDN[t, (k)^2]], {t, 0, EllipticK[(k)^2]}, GenerateConditions->None] == Divide[1,2]*EllipticK[(k)^2]*Log[Sqrt[1 - (k)^(2)]] |
Failure | Failure | Error | Skipped - Because timed out |
| 22.15.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{\xi}{k} = x} | JacobiSN(xi, k) = x |
JacobiSN[\[Xi], (k)^2] == x |
Failure | Failure | Failed [30 / 30] 30/30]: [[.2924027565+.2435601371*I <- {x = 1/2, xi = 1/2*3^(1/2)+1/2*I, k = 1}.1797898601-.1565493762e-1*I <- {x = 1/2, xi = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [30 / 30]
{Complex[0.29240275641803626, 0.2435601371571337] <- {Rule[k, 1], Rule[x, 0.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.17978986006074704, -0.015654937469336286] <- {Rule[k, 2], Rule[x, 0.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.15.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{\eta}{k} = x} | JacobiCN(eta, k) = x |
JacobiCN[\[Eta], (k)^2] == x |
Failure | Failure | Failed [30 / 30] 30/30]: [[.2107428373-.2715436778*I <- {eta = 1/2*3^(1/2)+1/2*I, x = 1/2, k = 1}.2337173832+.1450431473e-1*I <- {eta = 1/2*3^(1/2)+1/2*I, x = 1/2, k = 2} |
Failed [30 / 30]
{Complex[0.21074283744314704, -0.27154367778248023] <- {Rule[k, 1], Rule[x, 0.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.23371738317128377, 0.01450431459800293] <- {Rule[k, 2], Rule[x, 0.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.15.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{\zeta}{k} = x} | JacobiDN(zeta, k) = x |
JacobiDN[\[Zeta], (k)^2] == x |
Successful | Successful | - | Successful [Tested: 1] |
| 22.15.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -K \leq \aJacobiellsnk@{x}{k}} | - EllipticK(k) <= InverseJacobiSN(x, k) |
- EllipticK[(k)^2] <= InverseJacobiSN[x, (k)^2] |
Failure | Failure | Error | Failed [9 / 9]
{LessEqual[DirectedInfinity[], Complex[0.8047189562170503, -1.5707963267948966]] <- {Rule[k, 1], Rule[x, 1.5]}LessEqual[Complex[-0.8428751774062981, 1.0782578237498217], Complex[0.372543189356477, -1.0782578237498215]] <- {Rule[k, 2], Rule[x, 1.5]} |
| 22.15.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellsnk@{x}{k} \leq K} | InverseJacobiSN(x, k) <= EllipticK(k) |
InverseJacobiSN[x, (k)^2] <= EllipticK[(k)^2] |
Failure | Failure | Error | Failed [9 / 9]
{LessEqual[Complex[0.8047189562170503, -1.5707963267948966], DirectedInfinity[]] <- {Rule[k, 1], Rule[x, 1.5]}LessEqual[Complex[0.372543189356477, -1.0782578237498215], Complex[0.8428751774062981, -1.0782578237498217]] <- {Rule[k, 2], Rule[x, 1.5]} |
| 22.15.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 \leq \aJacobiellcnk@{x}{k}} | 0 <= InverseJacobiCN(x, k) |
0 <= InverseJacobiCN[x, (k)^2] |
Failure | Failure | Successful [Tested: 9] | Failed [8 / 9]
{LessEqual[0.0, Complex[0.0, 0.8410686705679303]] <- {Rule[k, 1], Rule[x, 1.5]}LessEqual[0.0, Complex[5.551115123125783*^-16, 0.6872864564092609]] <- {Rule[k, 2], Rule[x, 1.5]} |
| 22.15.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellcnk@{x}{k} \leq 2K} | InverseJacobiCN(x, k) <= 2*EllipticK(k) |
InverseJacobiCN[x, (k)^2] <= 2*EllipticK[(k)^2] |
Failure | Failure | Error | Failed [9 / 9]
{LessEqual[Complex[0.0, 0.8410686705679303], DirectedInfinity[]] <- {Rule[k, 1], Rule[x, 1.5]}LessEqual[Complex[5.551115123125783*^-16, 0.6872864564092609], Complex[1.6857503548125963, -2.1565156474996434]] <- {Rule[k, 2], Rule[x, 1.5]} |
| 22.15.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 \leq \aJacobielldnk@{x}{k}} | 0 <= InverseJacobiDN(x, k) |
0 <= InverseJacobiDN[x, (k)^2] |
Failure | Failure | Successful [Tested: 9] | Failed [8 / 9]
{LessEqual[0.0, Complex[0.0, 0.8410686705679303]] <- {Rule[k, 1], Rule[x, 1.5]}LessEqual[0.0, Complex[1.6857503548125963, -1.6950867772240739]] <- {Rule[k, 2], Rule[x, 1.5]} |
| 22.15.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobielldnk@{x}{k} \leq K} | InverseJacobiDN(x, k) <= EllipticK(k) |
InverseJacobiDN[x, (k)^2] <= EllipticK[(k)^2] |
Failure | Failure | Error | Failed [9 / 9]
{LessEqual[Complex[0.0, 0.8410686705679303], DirectedInfinity[]] <- {Rule[k, 1], Rule[x, 1.5]}LessEqual[Complex[1.6857503548125963, -1.6950867772240739], Complex[0.8428751774062981, -1.0782578237498217]] <- {Rule[k, 2], Rule[x, 1.5]} |
| 22.15.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \xi = (-1)^{m}\aJacobiellsnk@{x}{k}+2mK} | xi = (- 1)^(m)* InverseJacobiSN(x, k)+ 2*m*K |
\[Xi] == (- 1)^(m)* InverseJacobiSN[x, (k)^2]+ 2*m*K |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.613064478e-1-2.070796327*I <- {K = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = 1/2*3^(1/2)+1/2*I, k = 1, m = 1}-3.402795168+.70796327e-1*I <- {K = 1/2*3^(1/2)+1/2*I, x = 3/2, xi = 1/2*3^(1/2)+1/2*I, k = 1, m = 2} |
Failed [300 / 300]
{Complex[-0.061306447567388456, -2.0707963267948966] <- {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-3.4027951675703663, 0.07079632679489672] <- {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[x, 1.5], Rule[ξ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.15.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta = +\aJacobiellcnk@{x}{k}+4mK} | eta = + InverseJacobiCN(x, k)+ 4*m*K |
\[Eta] == + InverseJacobiCN[x, (k)^2]+ 4*m*K |
Failure | Failure | Failed [300 / 300] 300/300]: [[-2.598076212-2.341068671*I <- {K = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 1}-6.062177828-4.341068671*I <- {K = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 2} |
Failed [300 / 300]
{Complex[-2.598076211353316, -2.34106867056793] <- {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-6.062177826491071, -4.34106867056793] <- {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.15.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta = -\aJacobiellcnk@{x}{k}+4mK} | eta = - InverseJacobiCN(x, k)+ 4*m*K |
\[Eta] == - InverseJacobiCN[x, (k)^2]+ 4*m*K |
Failure | Failure | Failed [300 / 300] 300/300]: [[-2.598076212-.6589313294*I <- {K = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 1}-6.062177828-2.658931329*I <- {K = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 2} |
Failed [300 / 300]
{Complex[-2.598076211353316, -0.6589313294320696] <- {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-6.062177826491071, -2.658931329432069] <- {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.15.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = +\aJacobielldnk@{x}{k}+2mK} | zeta = + InverseJacobiDN(x, k)+ 2*m*K |
\[Zeta] == + InverseJacobiDN[x, (k)^2]+ 2*m*K |
Failure | Failure | Failed [270 / 270] 270/270]: [[-1.732050808-1.000000000*I <- {K = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 1}-3.464101616-2.*I <- {K = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 2} |
Failed [270 / 270]
{Complex[-1.7320508075688774, -0.9999999999999999] <- {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[x, 1.5]}Complex[-3.464101615137755, -1.9999999999999998] <- {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[x, 1.5]} |
| 22.15.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \zeta = -\aJacobielldnk@{x}{k}+2mK} | zeta = - InverseJacobiDN(x, k)+ 2*m*K |
\[Zeta] == - InverseJacobiDN[x, (k)^2]+ 2*m*K |
Failure | Failure | Failed [270 / 270] 270/270]: [[-1.732050808+.682137341*I <- {K = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 1}-3.464101616-.317862659*I <- {K = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1, m = 2} |
Failed [270 / 270]
{Complex[-1.7320508075688774, 0.6821373411358608] <- {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 1], Rule[x, 1.5]}Complex[-3.464101615137755, -0.3178626588641391] <- {Rule[k, 1], Rule[K, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[m, 2], Rule[x, 1.5]} |
| 22.15.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = \int_{0}^{\Jacobiellsnk@{x}{k}}\frac{\diff{t}}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}}} | x = int((1)/(sqrt((1 - (t)^(2))*(1 - (k)^(2)* (t)^(2)))), t = 0..JacobiSN(x, k)) |
x == Integrate[Divide[1,Sqrt[(1 - (t)^(2))*(1 - (k)^(2)* (t)^(2))]], {t, 0, JacobiSN[x, (k)^2]}, GenerateConditions->None] |
Failure | Aborted | Successful [Tested: 1] | Skipped - Because timed out |
| 22.15.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellsnk@{x}{k} = \int_{0}^{x}\frac{\diff{t}}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}}} | InverseJacobiSN(x, k) = int((1)/(sqrt((1 - (t)^(2))*(1 - (k)^(2)* (t)^(2)))), t = 0..x) |
InverseJacobiSN[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 - (t)^(2))*(1 - (k)^(2)* (t)^(2))]], {t, 0, x}, GenerateConditions->None] |
Error | Aborted | - | Skipped - Because timed out |
| 22.15.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellcnk@{x}{k} = \int_{x}^{1}\frac{\diff{t}}{\sqrt{(1-t^{2})({k^{\prime}}^{2}+k^{2}t^{2})}}} | InverseJacobiCN(x, k) = int((1)/(sqrt((1 - (t)^(2))*(1 - (k)^(2)+ (k)^(2)* (t)^(2)))), t = x..1) |
InverseJacobiCN[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 - (t)^(2))*(1 - (k)^(2)+ (k)^(2)* (t)^(2))]], {t, x, 1}, GenerateConditions->None] |
Error | Aborted | - | Skipped - Because timed out |
| 22.15.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobielldnk@{x}{k} = \int_{x}^{1}\frac{\diff{t}}{\sqrt{(1-t^{2})(t^{2}-{k^{\prime}}^{2})}}} | InverseJacobiDN(x, k) = int((1)/(sqrt((1 - (t)^(2))*((t)^(2)-1 - (k)^(2)))), t = x..1) |
InverseJacobiDN[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 - (t)^(2))*((t)^(2)-1 - (k)^(2))]], {t, x, 1}, GenerateConditions->None] |
Error | Aborted | - | Skipped - Because timed out |
| 22.15.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellcdk@{x}{k} = \int_{x}^{1}\frac{\diff{t}}{\sqrt{(1-t^{2})(1-k^{2}t^{2})}}} | InverseJacobiCD(x, k) = int((1)/(sqrt((1 - (t)^(2))*(1 - (k)^(2)* (t)^(2)))), t = x..1) |
InverseJacobiCD[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 - (t)^(2))*(1 - (k)^(2)* (t)^(2))]], {t, x, 1}, GenerateConditions->None] |
Failure | Aborted | Error | Skipped - Because timed out |
| 22.15.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellsdk@{x}{k} = \int_{0}^{x}\frac{\diff{t}}{\sqrt{(1-{k^{\prime}}^{2}t^{2})(1+k^{2}t^{2})}}} | InverseJacobiSD(x, k) = int((1)/(sqrt((1 -1 - (k)^(2)*(t)^(2))*(1 + (k)^(2)* (t)^(2)))), t = 0..x) |
InverseJacobiSD[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 -1 - (k)^(2)*(t)^(2))*(1 + (k)^(2)* (t)^(2))]], {t, 0, x}, GenerateConditions->None] |
Error | Failure | - | Skip - No test values generated |
| 22.15.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellndk@{x}{k} = \int_{1}^{x}\frac{\diff{t}}{\sqrt{(t^{2}-1)(1-{k^{\prime}}^{2}t^{2})}}} | InverseJacobiND(x, k) = int((1)/(sqrt(((t)^(2)- 1)*(1 -1 - (k)^(2)*(t)^(2)))), t = 1..x) |
InverseJacobiND[x, (k)^2] == Integrate[Divide[1,Sqrt[((t)^(2)- 1)*(1 -1 - (k)^(2)*(t)^(2))]], {t, 1, x}, GenerateConditions->None] |
Error | Failure | - | Skip - No test values generated |
| 22.15.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobielldck@{x}{k} = \int_{1}^{x}\frac{\diff{t}}{\sqrt{(t^{2}-1)(t^{2}-k^{2})}}} | InverseJacobiDC(x, k) = int((1)/(sqrt(((t)^(2)- 1)*((t)^(2)- (k)^(2)))), t = 1..x) |
InverseJacobiDC[x, (k)^2] == Integrate[Divide[1,Sqrt[((t)^(2)- 1)*((t)^(2)- (k)^(2))]], {t, 1, x}, GenerateConditions->None] |
Failure | Aborted | Error | Skipped - Because timed out |
| 22.15.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellnck@{x}{k} = \int_{1}^{x}\frac{\diff{t}}{\sqrt{(t^{2}-1)(k^{2}+{k^{\prime}}^{2}t^{2})}}} | InverseJacobiNC(x, k) = int((1)/(sqrt(((t)^(2)- 1)*((k)^(2)+1 - (k)^(2)*(t)^(2)))), t = 1..x) |
InverseJacobiNC[x, (k)^2] == Integrate[Divide[1,Sqrt[((t)^(2)- 1)*((k)^(2)+1 - (k)^(2)*(t)^(2))]], {t, 1, x}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.15.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellsck@{x}{k} = \int_{0}^{x}\frac{\diff{t}}{\sqrt{(1+t^{2})(1+{k^{\prime}}^{2}t^{2})}}} | InverseJacobiSC(x, k) = int((1)/(sqrt((1 + (t)^(2))*(1 +1 - (k)^(2)*(t)^(2)))), t = 0..x) |
InverseJacobiSC[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 + (t)^(2))*(1 +1 - (k)^(2)*(t)^(2))]], {t, 0, x}, GenerateConditions->None] |
Error | Aborted | - | Skipped - Because timed out |
| 22.15.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellnsk@{x}{k} = \int_{x}^{\infty}\frac{\diff{t}}{\sqrt{(t^{2}-1)(t^{2}-k^{2})}}} | InverseJacobiNS(x, k) = int((1)/(sqrt(((t)^(2)- 1)*((t)^(2)- (k)^(2)))), t = x..infinity) |
InverseJacobiNS[x, (k)^2] == Integrate[Divide[1,Sqrt[((t)^(2)- 1)*((t)^(2)- (k)^(2))]], {t, x, Infinity}, GenerateConditions->None] |
Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 22.15.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobielldsk@{x}{k} = \int_{x}^{\infty}\frac{\diff{t}}{\sqrt{(t^{2}+k^{2})(t^{2}-{k^{\prime}}^{2})}}} | InverseJacobiDS(x, k) = int((1)/(sqrt(((t)^(2)+ (k)^(2))*((t)^(2)-1 - (k)^(2)))), t = x..infinity) |
InverseJacobiDS[x, (k)^2] == Integrate[Divide[1,Sqrt[((t)^(2)+ (k)^(2))*((t)^(2)-1 - (k)^(2))]], {t, x, Infinity}, GenerateConditions->None] |
Error | Aborted | - | Skipped - Because timed out |
| 22.15.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \aJacobiellcsk@{x}{k} = \int_{x}^{\infty}\frac{\diff{t}}{\sqrt{(1+t^{2})(t^{2}+{k^{\prime}}^{2})}}} | InverseJacobiCS(x, k) = int((1)/(sqrt((1 + (t)^(2))*((t)^(2)+1 - (k)^(2)))), t = x..infinity) |
InverseJacobiCS[x, (k)^2] == Integrate[Divide[1,Sqrt[(1 + (t)^(2))*((t)^(2)+1 - (k)^(2))]], {t, x, Infinity}, GenerateConditions->None] |
Error | Aborted | - | Skipped - Because timed out |
| 22.16.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{x}{k} = \Asin@{\Jacobiellsnk@{x}{k}}} | Error |
JacobiAmplitude[x, Power[k, 2]] == ArcSin[JacobiSN[x, (k)^2]] |
Missing Macro Error | Failure | - | Failed [1 / 3]
{6.283185307179586 <- {Rule[k, 3], Rule[x, Rational[3, 2]]} |
| 22.16.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{x+2K}{k} = \Jacobiamk@{x}{k}+\pi} | JacobiAM(x + 2*EllipticK(k), k) = JacobiAM(x, k)+ Pi |
JacobiAmplitude[x + 2*EllipticK[(k)^2], Power[k, 2]] == JacobiAmplitude[x, Power[k, 2]]+ Pi |
Failure | Failure | Error | Failed [1 / 3]
{Plus[-4.273320998840302, Gudermannian[DirectedInfinity[]]] <- {Rule[k, 1], Rule[x, Rational[3, 2]]} |
| 22.16.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{x}{k} = \int_{0}^{x}\Jacobielldnk@{t}{k}\diff{t}} | JacobiAM(x, k) = int(JacobiDN(t, k), t = 0..x) |
JacobiAmplitude[x, Power[k, 2]] == Integrate[JacobiDN[t, (k)^2], {t, 0, x}, GenerateConditions->None] |
Failure | Successful | Successful [Tested: 9] | Successful [Tested: 9] |
| 22.16.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{x}{0} = x} | JacobiAM(x, 0) = x |
JacobiAmplitude[x, Power[0, 2]] == x |
Successful | Successful | - | Successful [Tested: 3] |
| 22.16.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{x}{1} = \Gudermannian@{x}} | JacobiAM(x, 1) = arctan(sinh(x)) |
JacobiAmplitude[x, Power[1, 2]] == Gudermannian[x] |
Failure | Successful | Successful [Tested: 3] | Successful [Tested: 3] |
| 22.16.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{x}{k} = \frac{\pi}{2K}x+2\sum_{n=1}^{\infty}\frac{q^{n}\sin@{2n\zeta}}{n(1+q^{2n})}} | JacobiAM(x, k) = (Pi)/(2*EllipticK(k))*x + 2*sum(((q)^(n)* sin(2*n*zeta))/(n*(1 + (q)^(2*n))), n = 1..infinity) |
JacobiAmplitude[x, Power[k, 2]] == Divide[Pi,2*EllipticK[(k)^2]]*x + 2*Sum[Divide[(q)^(n)* Sin[2*n*\[Zeta]],n*(1 + (q)^(2*n))], {n, 1, Infinity}, GenerateConditions->None] |
Failure | Failure | Skipped - Because timed out | Failed [30 / 30]
{Plus[Complex[1.9977537490349477, 0.49999999999999994], Times[-1.0, Gudermannian[DirectedInfinity[]]]] <- {Rule[k, 1], Rule[x, Rational[3, 2]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.6288351638274511, -0.8359897636003678] <- {Rule[k, 2], Rule[x, Rational[3, 2]], Rule[ζ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.16.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = \incellintFk@{\phi}{k}} | x = EllipticF(sin(phi), k) |
x == EllipticF[\[Phi], (k)^2] |
Failure | Failure | Failed [90 / 90] 90/90]: [[.6791299710-.6773780507*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}1.016811658-.7182528229*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 2} |
Failed [90 / 90]
{Complex[0.6791299712710547, -0.6773780505641274] <- {Rule[k, 1], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.0168116579433883, -0.7182528227883367] <- {Rule[k, 2], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.16.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{x}{k} = \phi} | JacobiAM(x, k) = phi |
JacobiAmplitude[x, Power[k, 2]] == \[Phi] |
Failure | Failure | Failed [90 / 90] 90/90]: [[.2657029410-.5000000000*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}-.6844899651-.5000000000*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 2} |
Failed [30 / 30]
{Complex[0.26570294146607043, -0.49999999999999994] <- {Rule[k, 1], Rule[x, Rational[3, 2]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.6844899649247672, -0.49999999999999994] <- {Rule[k, 2], Rule[x, Rational[3, 2]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.16.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{x}{k} = \sin@@{\phi}} | JacobiSN(x, k) = sin(phi) |
JacobiSN[x, (k)^2] == Sin[\[Phi]] |
Failure | Failure | Failed [90 / 90] 90/90]: [[.461679191e-1-.3375964631*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}-.6784403409-.3375964631*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 2} |
Failed [90 / 90]
{Complex[0.046167919344728525, -0.33759646322287] <- {Rule[k, 1], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.678440340667692, -0.33759646322287] <- {Rule[k, 2], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.16.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@@{\phi} = \sin@{\Jacobiamk@{x}{k}}} | sin(phi) = sin(JacobiAM(x, k)) |
Sin[\[Phi]] == Sin[JacobiAmplitude[x, Power[k, 2]]] |
Failure | Failure | Failed [90 / 90] 90/90]: [[-.461679191e-1+.3375964631*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}.6784403409+.3375964631*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 2} |
Failed [30 / 30]
{Complex[-0.046167919344728525, 0.33759646322287] <- {Rule[k, 1], Rule[x, Rational[3, 2]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.678440340667692, 0.33759646322287] <- {Rule[k, 2], Rule[x, Rational[3, 2]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.16.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{x}{k} = \cos@@{\phi}} | JacobiCN(x, k) = cos(phi) |
JacobiCN[x, (k)^2] == Cos[\[Phi]] |
Failure | Failure | Failed [90 / 90] 90/90]: [[-.3054469840+.3969495503*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}.2530246253+.3969495503*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 2} |
Failed [90 / 90]
{Complex[-0.3054469841149447, 0.3969495502290325] <- {Rule[k, 1], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.2530246251336542, 0.3969495502290325] <- {Rule[k, 2], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.16.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\phi} = \cos@{\Jacobiamk@{x}{k}}} | cos(phi) = cos(JacobiAM(x, k)) |
Cos[\[Phi]] == Cos[JacobiAmplitude[x, Power[k, 2]]] |
Failure | Failure | Failed [90 / 90] 90/90]: [[.3054469840-.3969495503*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}-.2530246253-.3969495503*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 2} |
Failed [30 / 30]
{Complex[0.3054469841149447, -0.3969495502290325] <- {Rule[k, 1], Rule[x, Rational[3, 2]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.2530246251336542, -0.3969495502290325] <- {Rule[k, 2], Rule[x, Rational[3, 2]], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.16.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \JacobiZetak@{x+K}{k} = \JacobiZetak@{x}{k}-k^{2}\Jacobiellsnk@{x}{k}\Jacobiellcdk@{x}{k}} | JacobiZeta(x + EllipticK(k), k) = JacobiZeta(x, k)- (k)^(2)* JacobiSN(x, k)*JacobiCD(x, k) |
JacobiZeta[x + EllipticK[(k)^2], k] == JacobiZeta[x, k]- (k)^(2)* JacobiSN[x, (k)^2]*JacobiCD[x, (k)^2] |
Failure | Failure | Error | Failed [9 / 9]
{Plus[-0.09234673295918805, JacobiZeta[DirectedInfinity[], 1.0]] <- {Rule[k, 1], Rule[x, 1.5]}Complex[-2.7319699839312124, -0.6260098794347219] <- {Rule[k, 2], Rule[x, 1.5]} |
| 22.16.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \JacobiZetak@{x+2K}{k} = \JacobiZetak@{x}{k}} | JacobiZeta(x + 2*EllipticK(k), k) = JacobiZeta(x, k) |
JacobiZeta[x + 2*EllipticK[(k)^2], k] == JacobiZeta[x, k] |
Successful | Failure | - | Failed [9 / 9]
{Plus[-0.9974949866040544, JacobiZeta[DirectedInfinity[], 1.0]] <- {Rule[k, 1], Rule[x, 1.5]}Complex[-0.2870190432201134, -5.437509139287473] <- {Rule[k, 2], Rule[x, 1.5]} |
| 22.17.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genJacobiellk{p}{q}@{z}{k} = \genJacobiellk{p}{q}@{z}{-k}} | genJacobiellk(p)*q* z*k = genJacobiellk(p)*q* z- k |
genJacobiellk(p)*q* z*k == genJacobiellk(p)*q* z- k |
Failure | Failure | Error | Failed [300 / 300]
{1.0 <- {Rule[k, 1], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[2.0, Times[Complex[0.0, 1.0], genJacobiellk]] <- {Rule[k, 2], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.17.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{z}{1/k} = k\Jacobiellsnk@{z/k}{k}} | JacobiSN(z, 1/ k) = k*JacobiSN(z/ k, k) |
JacobiSN[z, (1/ k)^2] == k*JacobiSN[z/ k, (k)^2] |
Failure | Failure | Successful [Tested: 21] | Successful [Tested: 21] |
| 22.17.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{z}{1/k} = \Jacobielldnk@{z/k}{k}} | JacobiCN(z, 1/ k) = JacobiDN(z/ k, k) |
JacobiCN[z, (1/ k)^2] == JacobiDN[z/ k, (k)^2] |
Failure | Failure | Successful [Tested: 21] | Successful [Tested: 21] |
| 22.17.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{z}{1/k} = \Jacobiellcnk@{z/k}{k}} | JacobiDN(z, 1/ k) = JacobiCN(z/ k, k) |
JacobiDN[z, (1/ k)^2] == JacobiCN[z/ k, (k)^2] |
Failure | Failure | Successful [Tested: 21] | Successful [Tested: 21] |
| 22.18.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(x^{2}/a^{2}\right)+\left(y^{2}/b^{2}\right) = 1} | ((x)^(2)/ (a)^(2))+((y)^(2)/ (b)^(2)) = 1 |
((x)^(2)/ (a)^(2))+((y)^(2)/ (b)^(2)) == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.18#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = a\Jacobiellsnk@{u}{k}} | x = a*JacobiSN(u, k) |
x == a*JacobiSN[u, (k)^2] |
Failure | Failure | Failed [300 / 300] 300/300]: [[2.688604135+.3653402056*I <- {a = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 1}2.519684790-.2348240643e-1*I <- {a = -3/2, u = 1/2*3^(1/2)+1/2*I, x = 3/2, k = 2} |
Failed [300 / 300]
{Complex[2.688604134627054, 0.3653402057357006] <- {Rule[a, -1.5], Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]}Complex[2.5196847900911203, -0.02348240620400443] <- {Rule[a, -1.5], Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]} |
| 22.18#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = b\Jacobiellcnk@{u}{k}} | y = b*JacobiCN(u, k) |
y == b*JacobiCN[u, (k)^2] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.433885744-.4073155167*I <- {b = -3/2, u = 1/2*3^(1/2)+1/2*I, y = -3/2, k = 1}-.399423925+.2175647210e-1*I <- {b = -3/2, u = 1/2*3^(1/2)+1/2*I, y = -3/2, k = 2} |
Failed [300 / 300]
{Complex[-0.43388574383527945, -0.40731551667372035] <- {Rule[b, -1.5], Rule[k, 1], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5]}Complex[-0.39942392524307424, 0.021756471897004394] <- {Rule[b, -1.5], Rule[k, 2], Rule[u, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[y, -1.5]} |
| 22.18.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle l(r) = (1/\sqrt{2})\aJacobiellcnk@{r}{1/\sqrt{2}}} | l*(r) = (1/(sqrt(2)))* InverseJacobiCN(r, 1/(sqrt(2))) |
l*(r) == (1/(Sqrt[2]))* InverseJacobiCN[r, (1/(Sqrt[2]))^2] |
Failure | Failure | Failed [18 / 18] 18/18]: [[-4.122057553+.6299669258*I <- {r = -3/2, l = 1}-5.622057553+.6299669258*I <- {r = -3/2, l = 2} |
Failed [18 / 18]
{Complex[-4.12205755429212, 0.629966925905157] <- {Rule[l, 1], Rule[r, -1.5]}Complex[-5.62205755429212, 0.629966925905157] <- {Rule[l, 2], Rule[r, -1.5]} |
| 22.18.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = \Jacobiellcnk@{\sqrt{2}l}{1/\sqrt{2}}} | r = JacobiCN(sqrt(2)*l, 1/(sqrt(2))) |
r == JacobiCN[Sqrt[2]*l, (1/(Sqrt[2]))^2] |
Failure | Failure | Failed [18 / 18] 18/18]: [[-1.810737930 <- {r = -3/2, l = 1}-.8262668012 <- {r = -3/2, l = 2} |
Failed [18 / 18]
{-1.810737930333856 <- {Rule[l, 1], Rule[r, -1.5]}-0.8262668010254658 <- {Rule[l, 2], Rule[r, -1.5]} |
| 22.18#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = \Jacobiellcnk@{\sqrt{2}l}{1/\sqrt{2}}\Jacobielldnk@{\sqrt{2}l}{1/\sqrt{2}}} | x = JacobiCN(sqrt(2)*l, 1/(sqrt(2)))*JacobiDN(sqrt(2)*l, 1/(sqrt(2))) |
x == JacobiCN[Sqrt[2]*l, (1/(Sqrt[2]))^2]*JacobiDN[Sqrt[2]*l, (1/(Sqrt[2]))^2] |
Failure | Failure | Failed [9 / 9] 9/9]: [[1.269911408 <- {x = 3/2, l = 1}2.074437352 <- {x = 3/2, l = 2} |
Failed [9 / 9]
{1.2699114077583538 <- {Rule[l, 1], Rule[x, 1.5]}2.0744373520381156 <- {Rule[l, 2], Rule[x, 1.5]} |
| 22.18.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle ax^{2}y^{2}+b(x^{2}y+xy^{2})+c(x^{2}+y^{2})+2dxy+e(x+y)+f = 0} | a*(x)^(2)* (y)^(2)+ b*((x)^(2)* y + x*(y)^(2))+ c*((x)^(2)+ (y)^(2))+ 2*d*x*y + exp(1)*(x + y)+ f = 0 |
a*(x)^(2)* (y)^(2)+ b*((x)^(2)* y + x*(y)^(2))+ c*((x)^(2)+ (y)^(2))+ 2*d*x*y + E*(x + y)+ f == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.18#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{3} = \frac{x_{1}y_{2}+x_{2}y_{1}}{1-k^{2}x_{1}^{2}x_{2}^{2}}} | (x[1]*y[2]+ x[2]*y[1])/(1 - (k)^(2)* x(x[1])^(2)*x(x[2])^(2)) |
Divide[Subscript[x, 1]*Subscript[y, 2]+ Subscript[x, 2]*Subscript[y, 1],1 - (k)^(2)* x(Subscript[x, 1])^(2)*x(Subscript[x, 2])^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.18#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y_{3} = \frac{y_{1}y_{2}+x_{2}(-(1+k^{2})x_{1}+2k^{2}x_{1}^{3})}{1-k^{2}x_{1}^{2}x_{2}^{2}}+x_{3}\frac{2k^{2}x_{1}y_{1}x_{2}^{2}}{1-k^{2}x_{1}^{2}x_{2}^{2}}} | (2*(k)^(2)* x[1]*y[1]*x(x[2])^(2))/(1 - (k)^(2)* x(x[1])^(2)*x(x[2])^(2)) |
Divide[2*(k)^(2)* Subscript[x, 1]*Subscript[y, 1]*x(Subscript[x, 2])^(2),1 - (k)^(2)* x(Subscript[x, 1])^(2)*x(Subscript[x, 2])^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.19.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{\theta(t)}{t} = -\sin@@{\theta(t)}} | diff(theta*(t), [t$(2)]) = - sin(theta*(t)) |
D[\[Theta]*(t), {t, 2}] == - Sin[\[Theta]*(t)] |
Failure | Failure | Failed [60 / 60] 60/60]: [[-1.247168970-.2207308174*I <- {t = -3/2, theta = 1/2*3^(1/2)+1/2*I}1.342338585-1.241300956*I <- {t = -3/2, theta = -1/2+1/2*I*3^(1/2)} |
Failed [60 / 60]
{Complex[-1.247168970138959, -0.22073081765616068] <- {Rule[t, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[1.3423385844153726, -1.2413009551766627] <- {Rule[t, -1.5], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 22.19.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{\tfrac{1}{2}\theta(t)} = \sin@{\frac{1}{2}\alpha}\Jacobiellsnk@{t+K}{\sin@{\tfrac{1}{2}\alpha}}} | sin((1)/(2)*theta*(t)) = sin((1)/(2)*alpha)*JacobiSN(t + EllipticK(k), sin((1)/(2)*alpha)) |
Sin[Divide[1,2]*\[Theta]*(t)] == Sin[Divide[1,2]*\[Alpha]]*JacobiSN[t + EllipticK[(k)^2], (Sin[Divide[1,2]*\[Alpha]])^2] |
Failure | Failure | Error | Failed [300 / 300]
{Plus[Complex[-0.6478293894548304, -0.30568930559799934], Times[-0.6816387600233341, JacobiSN[DirectedInfinity[], 0.4646313991661485]]] <- {Rule[k, 1], Rule[t, -1.5], Rule[α, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.12355997139036334, 0.2467451262932382] <- {Rule[k, 2], Rule[t, -1.5], Rule[α, 1.5], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.19.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \theta(t) = 2\Jacobiamk@{t\sqrt{E/2}}{\sqrt{2/E}}} | theta*(t) = 2*JacobiAM(t*sqrt(E/ 2), sqrt(2/ E)) |
\[Theta]*(t) == 2*JacobiAmplitude[t*Sqrt[E/ 2], Power[Sqrt[2/ E], 2]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[.133442481-.3164102922*I <- {E = 1/2*3^(1/2)+1/2*I, t = -3/2, theta = 1/2*3^(1/2)+1/2*I}2.182480587-.8654483982*I <- {E = 1/2*3^(1/2)+1/2*I, t = -3/2, theta = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[0.13344248094652933, -0.31641029231150586] <- {Rule[E, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[t, -1.5], Rule[x, Rational[3, 2]], Rule[θ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[2.182480586623187, -0.865448397988164] <- {Rule[E, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[t, -1.5], Rule[x, Rational[3, 2]], Rule[θ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 22.19.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{x(t)}{t} = -\deriv{V(x)}{x}} | diff(x*(t), [t$(2)]) = - diff(V*(x), x) |
D[x*(t), {t, 2}] == - D[V*(x), x] |
Failure | Failure | Failed [180 / 180] 180/180]: [[.8660254040+.5000000000*I <- {V = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2}.8660254040+.5000000000*I <- {V = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 1/2} |
Failed [180 / 180]
{Complex[0.8660254037844387, 0.49999999999999994] <- {Rule[t, -1.5], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 1.5]}Complex[0.8660254037844387, 0.49999999999999994] <- {Rule[t, -1.5], Rule[V, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, 0.5]} |
| 22.19.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle V(x) = +\tfrac{1}{2}x^{2}+\tfrac{1}{4}\beta x^{4}} | V*(x) = +(1)/(2)*(x)^(2)+(1)/(4)*beta*(x)^(4) |
V*(x) == +Divide[1,2]*(x)^(2)+Divide[1,4]*\[Beta]*(x)^(4) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.19.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x(t) = a\Jacobiellcnk@{t\sqrt{1+2\eta}}{k}} | x*(t) = a*JacobiCN(t*sqrt(1 + 2*eta), k) |
x*(t) == a*JacobiCN[t*Sqrt[1 + 2*\[Eta]], (k)^2] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-2.032489573-.1028075729*I <- {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 1}-1.103953626-.7415756720e-2*I <- {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 2} |
Failed [300 / 300]
{Complex[-2.032489572589819, -0.10280757291863922] <- {Rule[a, -1.5], Rule[k, 1], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-1.103953626215099, -0.007415756590236153] <- {Rule[a, -1.5], Rule[k, 2], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.19.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x(t) = a\Jacobiellsnk@{t\sqrt{1-\eta}}{k}} | x*(t) = a*JacobiSN(t*sqrt(1 - eta), k) |
x*(t) == a*JacobiSN[t*Sqrt[1 - \[Eta]], (k)^2] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-3.540811611+.4656977091*I <- {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 1}-3.440732980-.1498418752e-1*I <- {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 2} |
Failed [300 / 300]
{Complex[-3.5408116110434387, 0.46569770889881135] <- {Rule[a, -1.5], Rule[k, 1], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-3.4407329797279083, -0.014984187659583321] <- {Rule[a, -1.5], Rule[k, 2], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.19.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x(t) = a\Jacobielldnk@{t\sqrt{\eta}}{k}} | x*(t) = a*JacobiDN(t*sqrt(eta), k) |
x*(t) == a*JacobiDN[t*Sqrt[\[Eta]], (k)^2] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-1.613955183-.2329422536*I <- {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 1}-3.968457087-.6161541466*I <- {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 2} |
Failed [300 / 300]
{Complex[-1.6139551823182394, -0.23294225362869586] <- {Rule[a, -1.5], Rule[k, 1], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-3.968457085129692, -0.6161541479869231] <- {Rule[a, -1.5], Rule[k, 2], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.19.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x(t) = a\Jacobiellcnk@{t\sqrt{2\eta-1}}{k}} | x*(t) = a*JacobiCN(t*sqrt(2*eta - 1), k) |
x*(t) == a*JacobiCN[t*Sqrt[2*\[Eta]- 1], (k)^2] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-1.736815452-.4365167404*I <- {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 1}-.272323884+.8696505748*I <- {a = -3/2, eta = 1/2*3^(1/2)+1/2*I, t = -3/2, x = 3/2, k = 2} |
Failed [300 / 300]
{Complex[-1.7368154521565795, -0.4365167405198458] <- {Rule[a, -1.5], Rule[k, 1], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.27232388329398516, 0.8696505752545954] <- {Rule[a, -1.5], Rule[k, 2], Rule[t, -1.5], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.20#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n} = \tfrac{1}{2}\left(a_{n-1}+b_{n-1}\right)} | a[n] = (1)/(2)*(a[n - 1]+ b[n - 1]) |
Subscript[a, n] == Divide[1,2]*(Subscript[a, n - 1]+ Subscript[b, n - 1]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.20#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{n} = \left(a_{n-1}b_{n-1}\right)^{1/2}} | b[n] = (a[n - 1]*b[n - 1])^(1/ 2) |
Subscript[b, n] == (Subscript[a, n - 1]*Subscript[b, n - 1])^(1/ 2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.20#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{n} = \tfrac{1}{2}\left(a_{n-1}-b_{n-1}\right)} | c[n] = (1)/(2)*(a[n - 1]- b[n - 1]) |
Subscript[c, n] == Divide[1,2]*(Subscript[a, n - 1]- Subscript[b, n - 1]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.20.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi_{N} = 2^{N}a_{N}x} | phi[N] = (2)^(N)* a[N]*x |
Subscript[\[Phi], N] == (2)^(N)* Subscript[a, N]*x |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 22.20.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi_{n-1} = \frac{1}{2}\left(\phi_{n}+\asin@{\frac{c_{n}}{a_{n}}\sin@@{\phi_{n}}}\right)} | phi[n - 1] = (1)/(2)*(phi[n]+ arcsin((c[n])/(a[n])*sin(phi[n]))) |
Subscript[\[Phi], n - 1] == Divide[1,2]*(Subscript[\[Phi], n]+ ArcSin[Divide[Subscript[c, n],Subscript[a, n]]*Sin[Subscript[\[Phi], n]]]) |
Failure | Failure | Failed [276 / 300] 276/300]: [[-1.366025404+.3660254040*I <- {phi = 1/2*3^(1/2)+1/2*I, a[n] = 1/2*3^(1/2)+1/2*I, c[n] = 1/2*3^(1/2)+1/2*I, phi[n] = 1/2*3^(1/2)+1/2*I, phi[-1+n] = -1/2+1/2*I*3^(1/2), n = 1}-1.366025404+.3660254040*I <- {phi = 1/2*3^(1/2)+1/2*I, a[n] = 1/2*3^(1/2)+1/2*I, c[n] = 1/2*3^(1/2)+1/2*I, phi[n] = 1/2*3^(1/2)+1/2*I, phi[-1+n] = -1/2+1/2*I*3^(1/2), n = 2} |
Failed [276 / 300]
{Complex[1.3660254037844384, -0.36602540378443876] <- {Rule[n, 1], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, Plus[-1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}Complex[1.3660254037844384, -0.36602540378443876] <- {Rule[n, 2], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[c, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, Plus[-1, n]], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, n], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 22.20#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellsnk@{x}{k} = \sin@@{\phi_{0}}} | JacobiSN(x, k) = sin(phi[0]) |
JacobiSN[x, (k)^2] == Sin[Subscript[\[Phi], 0]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[.461679191e-1-.3375964631*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, phi[0] = 1/2*3^(1/2)+1/2*I, k = 1}-.6784403409-.3375964631*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, phi[0] = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[0.046167919344728525, -0.33759646322287] <- {Rule[k, 1], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-0.678440340667692, -0.33759646322287] <- {Rule[k, 2], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.20#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiellcnk@{x}{k} = \cos@@{\phi_{0}}} | JacobiCN(x, k) = cos(phi[0]) |
JacobiCN[x, (k)^2] == Cos[Subscript[\[Phi], 0]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.3054469840+.3969495503*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, phi[0] = 1/2*3^(1/2)+1/2*I, k = 1}.2530246253+.3969495503*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, phi[0] = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[-0.3054469841149447, 0.3969495502290325] <- {Rule[k, 1], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[0.2530246251336542, 0.3969495502290325] <- {Rule[k, 2], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.20#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobielldnk@{x}{k} = \frac{\cos@@{\phi_{0}}}{\cos@{\phi_{1}-\phi_{0}}}} | JacobiDN(x, k) = (cos(phi[0]))/(cos(phi[1]- phi[0])) |
JacobiDN[x, (k)^2] == Divide[Cos[Subscript[\[Phi], 0]],Cos[Subscript[\[Phi], 1]- Subscript[\[Phi], 0]]] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.3054469840+.3969495503*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, phi[0] = 1/2*3^(1/2)+1/2*I, phi[1] = 1/2*3^(1/2)+1/2*I, k = 1}-1.663077867+.3969495503*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, phi[0] = 1/2*3^(1/2)+1/2*I, phi[1] = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[-0.3054469841149447, 0.3969495502290325] <- {Rule[k, 1], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-1.6630778670906836, 0.3969495502290325] <- {Rule[k, 2], Rule[x, 1.5], Rule[ϕ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, 0], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[ϕ, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 22.20#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle K = \frac{\pi}{2M(1,k^{\prime})}} | EllipticK(k) = (Pi)/(2*M*(1 ,sqrt(1 - (k)^(2)))) |
EllipticK[(k)^2] == Divide[Pi,2*M*(1 ,Sqrt[1 - (k)^(2)])] |
Skipped - no semantic math | Skipped - no semantic math | - | - |