Results of Elliptic Integrals II: Difference between revisions
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Revision as of 19:00, 15 October 2020
This is the second half of the chapter Elliptic Integrals. It shows results from Section 19.22 to 19.36. For Section 19.1 to 19.21 go to Elliptic Integrals I.
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 19.22.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{0}{x^{2}}{y^{2}} = \CarlsonsymellintRF@{0}{xy}{a^{2}}} | 0.5*int(1/(sqrt(t+0)*sqrt(t+(x)^(2))*sqrt(t+(y)^(2))), t = 0..infinity) = 0.5*int(1/(sqrt(t+0)*sqrt(t+x*y)*sqrt(t+(a)^(2))), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]/Sqrt[(y)^(2)-0] == EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0] |
Aborted | Failure | Skipped - Because timed out | Failed [102 / 108]
{Complex[0.1731783664325578, 0.8740191847640398] <- {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}Complex[0.4406854652170371, 0.9732684211375591] <- {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -0.5]} |
| 19.22.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRG@{0}{x^{2}}{y^{2}} = 4\CarlsonsymellintRG@{0}{xy}{a^{2}}-xy\CarlsonsymellintRF@{0}{xy}{a^{2}}} | Error |
2*Sqrt[(y)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(y)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]+Cot[ArcCos[Sqrt[0/(y)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(y)^(2)]]]^2]) == 4*Sqrt[(a)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(a)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]+Cot[ArcCos[Sqrt[0/(a)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(a)^(2)]]]^2])- x*y*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0] |
Missing Macro Error | Failure | - | Failed [108 / 108]
{Complex[-0.848574889541176, -1.6278775384876862] <- {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}-2.356194490192345 <- {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.22.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2y^{2}\CarlsonsymellintRD@{0}{x^{2}}{y^{2}} = \tfrac{1}{4}(y^{2}-x^{2})\CarlsonsymellintRD@{0}{xy}{a^{2}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}} | Error |
2*(y)^(2)* 3*(EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/(((y)^(2)-(x)^(2))*((y)^(2)-0)^(1/2)) == Divide[1,4]*((y)^(2)- (x)^(2))* 3*(EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/(((a)^(2)-x*y)*((a)^(2)-0)^(1/2))+ 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0] |
Missing Macro Error | Failure | - | Failed [108 / 108]
{Indeterminate <- {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}Indeterminate <- {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.22.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)} | Error |
(p(Subscript[p, +])^(2)- p(Subscript[p, -])^(2))* 3*((y)^(2)-0)/((y)^(2)-(p)^(2))*(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == 3*((a)^(2)-0)/((a)^(2)-p(Subscript[p, +])^(2))*(EllipticPi[((a)^(2)-p(Subscript[p, +])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]- 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]+ 3*Pi/(2*p) |
Missing Macro Error | Failure | - | Error |
| 19.22.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{0}{xy}{a^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{0}{xy}{a^{2}}+3\pi/(2p)} | Error |
(p(Subscript[p, -])^(2)- p(Subscript[p, +])^(2))* 3*((y)^(2)-0)/((y)^(2)-(p)^(2))*(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == 3*((a)^(2)-0)/((a)^(2)-p(Subscript[p, -])^(2))*(EllipticPi[((a)^(2)-p(Subscript[p, -])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]- 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0]+ 3*Pi/(2*p) |
Missing Macro Error | Failure | - | Error |
| 19.22#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{+}p_{-} = pa} | p[+]*p[-] = p*a |
Subscript[p, +]*Subscript[p, -] == p*a |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{+}^{2}+p_{-}^{2} = p^{2}+xy} | (p[+])^(2)+ (p[-])^(2) = (p)^(2)+ x*y |
(Subscript[p, +])^(2)+ (Subscript[p, -])^(2) == (p)^(2)+ x*y |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{+}^{2}-p_{-}^{2} = \sqrt{(p^{2}-x^{2})(p^{2}-y^{2})}} | (p[+])^(2)- (p[-])^(2) = sqrt(((p)^(2)- (x)^(2))*((p)^(2)- (y)^(2))) |
(Subscript[p, +])^(2)- (Subscript[p, -])^(2) == Sqrt[((p)^(2)- (x)^(2))*((p)^(2)- (y)^(2))] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 4(p_{+}^{2}-a^{2}) = (\sqrt{p^{2}-x^{2}}+\sqrt{p^{2}-y^{2}})^{2}} | (p(p[+])^(2)- (a)^(2)) = (sqrt((p)^(2)- (x)^(2))+sqrt((p)^(2)- (y)^(2)))^(2) |
(p(Subscript[p, +])^(2)- (a)^(2)) == (Sqrt[(p)^(2)- (x)^(2)]+Sqrt[(p)^(2)- (y)^(2)])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2p^{2}\CarlsonsymellintRJ@{0}{x^{2}}{y^{2}}{p^{2}} = v_{+}v_{-}\CarlsonsymellintRJ@{0}{xy}{a^{2}}{v^{2}_{+}}+3\CarlsonsymellintRF@{0}{xy}{a^{2}}} | Error |
2*(p)^(2)* 3*((y)^(2)-0)/((y)^(2)-(p)^(2))*(EllipticPi[((y)^(2)-(p)^(2))/((y)^(2)-0),ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(y)^(2)]],((y)^(2)-(x)^(2))/((y)^(2)-0)])/Sqrt[(y)^(2)-0] == Subscript[v, +]*3*((a)^(2)-0)/((a)^(2)-v(Subscript[v, +])^(2))*(EllipticPi[((a)^(2)-v(Subscript[v, +])^(2))/((a)^(2)-0),ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]-EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)])/Sqrt[(a)^(2)-0]+ 3*EllipticF[ArcCos[Sqrt[0/(a)^(2)]],((a)^(2)-x*y)/((a)^(2)-0)]/Sqrt[(a)^(2)-0] |
Missing Macro Error | Failure | - | Error |
| 19.22.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} = \frac{1}{\AGM@{a_{0}}{g_{0}}}} | 0.5*int(1/(sqrt(t+0)*sqrt(t+a(a[0])^(2))*sqrt(t+g(g[0])^(2))), t = 0..infinity) = (1)/(GaussAGM(a[0], g[0])) |
Error |
Aborted | Missing Macro Error | Skipped - Because timed out | - |
| 19.22.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{0}^{2}-\sum_{n=0}^{\infty}2^{n-1}c_{n}^{2}\right) = \frac{1}{\AGM@{a_{0}}{g_{0}}}\left(a_{1}^{2}-\sum_{n=2}^{\infty}2^{n-1}c_{n}^{2}\right)} | (a(a[0])^(2)- sum((2)^(n - 1)* c(c[n])^(2), n = 0..infinity)) (a(a[1])^(2)- sum((2)^(n - 1)* c(c[n])^(2), n = 2..infinity)) |
Error |
Failure | Missing Macro Error | Error | - |
| 19.22#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{0} = 1} | Q[0] = 1 |
Subscript[Q, 0] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{n+1} = \tfrac{1}{2}Q_{n}\frac{a_{n}-g_{n}}{a_{n}+g_{n}}} | Q[n + 1] = (1)/(2)*Q[n]*(a[n]- g[n])/(a[n]+ g[n]) |
Subscript[Q, n + 1] == Divide[1,2]*Subscript[Q, n]*Divide[Subscript[a, n]- Subscript[g, n],Subscript[a, n]+ Subscript[g, n]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{n+1} = \frac{p_{n}^{2}+a_{n}g_{n}}{2p_{n}}} | p[n + 1] (p(p[n])^(2)+ a[n]*g[n])/(2*p[n]) |
Subscript[p, n + 1] Divide[p(Subscript[p, n])^(2)+ Subscript[a, n]*Subscript[g, n],2*Subscript[p, n]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \varepsilon_{n} = \frac{p_{n}^{2}-a_{n}g_{n}}{p_{n}^{2}+a_{n}g_{n}}} | (p(p[n])^(2)- a[n]*g[n])/(p(p[n])^(2)+ a[n]*g[n]) |
Divide[p(Subscript[p, n])^(2)- Subscript[a, n]*Subscript[g, n],p(Subscript[p, n])^(2)+ Subscript[a, n]*Subscript[g, n]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{0} = 1} | Q[0] = 1 |
Subscript[Q, 0] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{n+1} = \tfrac{1}{2}Q_{n}\varepsilon_{n}} | Q[n + 1] = (1)/(2)*Q[n]*varepsilon[n] |
Subscript[Q, n + 1] == Divide[1,2]*Subscript[Q, n]*Subscript[\[CurlyEpsilon], n] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle p_{0}^{2} = a_{0}^{2}(q_{0}^{2}+g_{0}^{2})/(q_{0}^{2}+a_{0}^{2})} | (p[0])^(2) (q(q[0])^(2)+ a(a[0])^(2)) |
(Subscript[p, 0])^(2) (q(Subscript[q, 0])^(2)+ a(Subscript[a, 0])^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a = (x+y)/2} | a = (x + y)/ 2 |
a == (x + y)/ 2 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2z_{+} = \sqrt{(z+x)(z+y)}+\sqrt{(z-x)(z-y)}} | 2*x + y*I[+] = sqrt(((x + y*I)+ x)*((x + y*I)+ y))+sqrt(((x + y*I)- x)*((x + y*I)- y)) |
2*Subscript[x + y*I, +] == Sqrt[((x + y*I)+ x)*((x + y*I)+ y)]+Sqrt[((x + y*I)- x)*((x + y*I)- y)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{+}z_{-} = za} | z[+]*z[-] = z*a |
Subscript[z, +]*Subscript[z, -] == z*a |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{+}^{2}+z_{-}^{2} = z^{2}+xy} | (x + y*I[+])^(2)+(x + y*I[-])^(2) = (x + y*I)^(2)+ x*y |
(Subscript[x + y*I, +])^(2)+(Subscript[x + y*I, -])^(2) == (x + y*I)^(2)+ x*y |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z_{+}^{2}-z_{-}^{2} = \sqrt{(z^{2}-x^{2})(z^{2}-y^{2})}} | (x + y*I[+])^(2)-(x + y*I[-])^(2) = sqrt(((x + y*I)^(2)- (x)^(2))*((x + y*I)^(2)- (y)^(2))) |
(Subscript[x + y*I, +])^(2)-(Subscript[x + y*I, -])^(2) == Sqrt[((x + y*I)^(2)- (x)^(2))*((x + y*I)^(2)- (y)^(2))] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 4(z_{+}^{2}-a^{2}) = (\sqrt{z^{2}-x^{2}}+\sqrt{z^{2}-y^{2}})^{2}} | ((x + y*I)(x + y*I[+])^(2)- (a)^(2)) = (sqrt((x + y*I)^(2)- (x)^(2))+sqrt((x + y*I)^(2)- (y)^(2)))^(2) |
((x + y*I)(Subscript[x + y*I, +])^(2)- (a)^(2)) == (Sqrt[(x + y*I)^(2)- (x)^(2)]+Sqrt[(x + y*I)^(2)- (y)^(2)])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}} = \CarlsonsymellintRF@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}} | 0.5*int(1/(sqrt(t+(a)^(2))*sqrt(t+(x + y*I)(x + y*I[-])^(2))*sqrt(t+(x + y*I)(x + y*I[+])^(2))), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, +])^(2)]],((x + y*I)(Subscript[x + y*I, +])^(2)-(x + y*I)(Subscript[x + y*I, -])^(2))/((x + y*I)(Subscript[x + y*I, +])^(2)-(a)^(2))]/Sqrt[(x + y*I)(Subscript[x + y*I, +])^(2)-(a)^(2)] |
Error | Failure | - | Error |
| 19.22.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z_{+}^{2}-z_{-}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{+}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{-}^{2}}{z_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)} | Error |
((x + y*I)(Subscript[x + y*I, +])^(2)-(x + y*I)(Subscript[x + y*I, -])^(2))* 3*(EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-EllipticE[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))])/(((x + y*I)^(2)-(y)^(2))*((x + y*I)^(2)-(x)^(2))^(1/2)) 3*(EllipticF[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, +])^(2)]],((x + y*I)(Subscript[x + y*I, +])^(2)-(x + y*I)(Subscript[x + y*I, -])^(2))/((x + y*I)(Subscript[x + y*I, +])^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, +])^(2)]],((x + y*I)(Subscript[x + y*I, +])^(2)-(x + y*I)(Subscript[x + y*I, -])^(2))/((x + y*I)(Subscript[x + y*I, +])^(2)-(a)^(2))])/(((x + y*I)(Subscript[x + y*I, +])^(2)-(x + y*I)(Subscript[x + y*I, -])^(2))*((x + y*I)(Subscript[x + y*I, +])^(2)-(a)^(2))^(1/2))- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+(3/(x + y*I)) |
Missing Macro Error | Failure | - | Error |
| 19.22.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z_{-}^{2}-z_{+}^{2})\CarlsonsymellintRD@{x^{2}}{y^{2}}{z^{2}} = {2(z_{-}^{2}-a^{2})}\CarlsonsymellintRD@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+(3/z)} | Error |
((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))* 3*(EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]-EllipticE[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))])/(((x + y*I)^(2)-(y)^(2))*((x + y*I)^(2)-(x)^(2))^(1/2)) 3*(EllipticF[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]],((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]],((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))])/(((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))*((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))^(1/2))- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+(3/(x + y*I)) |
Missing Macro Error | Failure | - | Error |
| 19.22.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p_{+}^{2}-p_{-}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{+}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{+}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}} | Error |
(p(Subscript[p, +])^(2)- p(Subscript[p, -])^(2))* 3*((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-p(Subscript[p, +])^(2))*(EllipticPi[((x + y*I)(Subscript[x + y*I, -])^(2)-p(Subscript[p, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2)),ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]],((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticF[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]],((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))])/Sqrt[(x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2)]- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+ 3*1/Sqrt[(p)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x + y*I)^(2))/((p)^(2))] |
Missing Macro Error | Failure | - | Error |
| 19.22.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p_{-}^{2}-p_{+}^{2})\CarlsonsymellintRJ@{x^{2}}{y^{2}}{z^{2}}{p^{2}} = 2(p_{-}^{2}-a^{2})\CarlsonsymellintRJ@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}{p_{-}^{2}}-3\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}+3\CarlsonellintRC@{z^{2}}{p^{2}}} | Error |
(p(Subscript[p, -])^(2)- p(Subscript[p, +])^(2))* 3*((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-p(Subscript[p, -])^(2))*(EllipticPi[((x + y*I)(Subscript[x + y*I, -])^(2)-p(Subscript[p, -])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2)),ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]],((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))]-EllipticF[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]],((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))])/Sqrt[(x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2)]- 3*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]+ 3*1/Sqrt[(p)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x + y*I)^(2))/((p)^(2))] |
Missing Macro Error | Failure | - | Error |
| 19.22.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRG@{x^{2}}{y^{2}}{z^{2}} = 4\CarlsonsymellintRG@{a^{2}}{z_{+}^{2}}{z_{-}^{2}}-xy\CarlsonsymellintRF@{x^{2}}{y^{2}}{z^{2}}-z} | Error |
2*Sqrt[(x + y*I)^(2)-(x)^(2)]*(EllipticE[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]+(Cot[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]]])^2*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]+Cot[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]]]^2]) Sqrt[(x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2)]*(EllipticE[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]],((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))]+(Cot[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]]])^2*EllipticF[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]],((x + y*I)(Subscript[x + y*I, -])^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))/((x + y*I)(Subscript[x + y*I, -])^(2)-(a)^(2))]+Cot[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(a)^(2)/(x + y*I)(Subscript[x + y*I, -])^(2)]]]^2])- x*y*EllipticF[ArcCos[Sqrt[(x)^(2)/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-(x)^(2))]/Sqrt[(x + y*I)^(2)-(x)^(2)]-(x + y*I) |
Missing Macro Error | Failure | - | Error |
| 19.22.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x^{2}}{y^{2}} = \CarlsonellintRC@{a^{2}}{ay}} | Error |
1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((y)^(2))] == 1/Sqrt[a*y]*Hypergeometric2F1[1/2,1/2,3/2,1-((a)^(2))/(a*y)] |
Missing Macro Error | Failure | - | Failed [108 / 108]
{Indeterminate <- {Rule[a, -1.5], Rule[x, 1.5], Rule[y, -1.5]}Indeterminate <- {Rule[a, -1.5], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.22#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x+y = 2a} | x + y = 2*a |
x + y == 2*a |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x-y = (\ifrac{2}{a})\sqrt{(a^{2}-z_{+}^{2})(a^{2}-z_{-}^{2})}} | x - y sqrt(((a)^(2)-(x + y*I)(x + y*I[+])^(2))*((a)^(2)-(x + y*I)(x + y*I[-])^(2))) |
x - y Sqrt[((a)^(2)-(x + y*I)(Subscript[x + y*I, +])^(2))*((a)^(2)-(x + y*I)(Subscript[x + y*I, -])^(2))] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.22#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = \ifrac{z_{+}z_{-}}{a}} | z = (z[+]*z[-])/(a) |
z == Divide[Subscript[z, +]*Subscript[z, -],a] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.23.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{0}{y}{z} = \int_{0}^{\pi/2}(y\cos^{2}@@{\theta}+z\sin^{2}@@{\theta})^{-1/2}\diff{\theta}} | 0.5*int(1/(sqrt(t+0)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) = int((y*(cos(theta))^(2)+(x + y*I)*(sin(theta))^(2))^(- 1/ 2), theta = 0..Pi/ 2) |
EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0] == Integrate[(y*(Cos[\[Theta]])^(2)+(x + y*I)*(Sin[\[Theta]])^(2))^(- 1/ 2), {\[Theta], 0, Pi/ 2}, GenerateConditions->None] |
Aborted | Failure | Skipped - Because timed out | Failed [18 / 18]
{Complex[0.8397393007192011, 1.792316631638506] <- {Rule[x, 1.5], Rule[y, -1.5]}Complex[-1.057179647328743, -0.8381019542468571] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.23.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRG@{0}{y}{z} = \frac{1}{2}\int_{0}^{\pi/2}(y\cos^{2}@@{\theta}+z\sin^{2}@@{\theta})^{1/2}\diff{\theta}} | Error |
Sqrt[x + y*I-0]*(EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]+(Cot[ArcCos[Sqrt[0/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]+Cot[ArcCos[Sqrt[0/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/x + y*I]]]^2]) == Divide[1,2]*Integrate[(y*(Cos[\[Theta]])^(2)+(x + y*I)*(Sin[\[Theta]])^(2))^(1/ 2), {\[Theta], 0, Pi/ 2}, GenerateConditions->None] |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Plus[Complex[0.5014070071339144, -0.6068932953779227], Times[Complex[1.345607733249115, -0.5573689727459014], Plus[Complex[1.465481142300126, -0.24396122198922798], Times[Complex[0.2643318009908678, -0.8730286325904596], Power[Plus[1.0, Times[Complex[-1.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, -1.5]}Plus[Complex[-0.9996439786591846, -0.22609983985234913], Times[Complex[1.345607733249115, 0.5573689727459014], Plus[Complex[1.0084590214609772, 0.7147093671486319], Times[Complex[0.2643318009908678, 0.8730286325904596], Power[Plus[1.0, Times[Complex[-1.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.23.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRD@{0}{y}{z} = 3\int_{0}^{\pi/2}(y\cos^{2}@@{\theta}+z\sin^{2}@@{\theta})^{-3/2}\sin^{2}@@{\theta}\diff{\theta}} | Error |
3*(EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/((x + y*I-y)*(x + y*I-0)^(1/2)) == 3*Integrate[(y*(Cos[\[Theta]])^(2)+(x + y*I)*(Sin[\[Theta]])^(2))^(- 3/ 2)* (Sin[\[Theta]])^(2), {\[Theta], 0, Pi/ 2}, GenerateConditions->None] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.23.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{0}{y}{z} = \frac{2}{\pi}\int_{0}^{\pi/2}\CarlsonellintRC@{y}{z\cos^{2}@@{\theta}}\diff{\theta}} | Error |
EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0] == Divide[2,Pi]*Integrate[1/Sqrt[(x + y*I)* (Cos[\[Theta]])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(y)/((x + y*I)* (Cos[\[Theta]])^(2))], {\[Theta], 0, Pi/ 2}, GenerateConditions->None] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.23.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\int_{0}^{\pi/2}\CarlsonellintRC@{y}{z\cos^{2}@@{\theta}}\diff{\theta} = \frac{2}{\pi}\int_{0}^{\infty}\CarlsonellintRC@{y\cosh^{2}@@{t}}{z}\diff{t}} | Error |
Divide[2,Pi]*Integrate[1/Sqrt[(x + y*I)* (Cos[\[Theta]])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(y)/((x + y*I)* (Cos[\[Theta]])^(2))], {\[Theta], 0, Pi/ 2}, GenerateConditions->None] == Divide[2,Pi]*Integrate[1/Sqrt[x + y*I]*Hypergeometric2F1[1/2,1/2,3/2,1-(y*(Cosh[t])^(2))/(x + y*I)], {t, 0, Infinity}, GenerateConditions->None] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.23.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{z} = \frac{2}{\pi}\int_{0}^{\pi/2}\CarlsonellintRC@{x}{y\cos^{2}@@{\theta}+z\sin^{2}@@{\theta}}\diff{\theta}} | Error |
EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] == Divide[2,Pi]*Integrate[1/Sqrt[y*(Cos[\[Theta]])^(2)+(x + y*I)* (Sin[\[Theta]])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y*(Cos[\[Theta]])^(2)+(x + y*I)* (Sin[\[Theta]])^(2))], {\[Theta], 0, Pi/ 2}, GenerateConditions->None] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.23.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 4\pi\CarlsonsymellintRF@{x}{y}{z} = \int_{0}^{2\pi}\!\!\!\!\int_{0}^{\pi}\frac{\sin@@{\theta}\diff{\theta}\diff{\phi}}{(x\sin^{2}@@{\theta}\cos^{2}@@{\phi}+y\sin^{2}@@{\theta}\sin^{2}@@{\phi}+z\cos^{2}@@{\theta})^{1/2}}} | 4*Pi*0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) = int(int((sin(theta))/((x*(sin(theta))^(2)* (cos(phi))^(2)+ y*(sin(theta))^(2)* (sin(phi))^(2)+(x + y*I)*(cos(theta))^(2))^(1/ 2)), theta = 0..Pi), phi = 0..2*Pi) |
4*Pi*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] == Integrate[Integrate[Divide[Sin[\[Theta]],(x*(Sin[\[Theta]])^(2)* (Cos[\[Phi]])^(2)+ y*(Sin[\[Theta]])^(2)* (Sin[\[Phi]])^(2)+(x + y*I)*(Cos[\[Theta]])^(2))^(1/ 2)], {\[Theta], 0, Pi}, GenerateConditions->None], {\[Phi], 0, 2*Pi}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.23.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRG@{x}{y}{z} = \frac{1}{4}\int_{0}^{\infty}\frac{1}{\sqrt{t+x}\sqrt{t+y}\sqrt{t+z}}\*\left(\frac{x}{t+x}+\frac{y}{t+y}+\frac{z}{t+z}\right)t\diff{t}} | Error |
Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) == Divide[1,4]*Integrate[Divide[1,Sqrt[t + x]*Sqrt[t + y]*Sqrt[t +(x + y*I)]]*(Divide[x,t + x]+Divide[y,t + y]+Divide[x + y*I,t +(x + y*I)])* t, {t, 0, Infinity}, GenerateConditions->None] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.24.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ln@@{4} \leq \sqrt{z}\CarlsonsymellintRF@{0}{y}{z}+\ln@@{\sqrt{y/z}}} | ln(4) <= sqrt(x + y*I)*0.5*int(1/(sqrt(t+0)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity)+ ln(sqrt(y/(x + y*I))) |
Log[4] <= Sqrt[x + y*I]*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0]+ Log[Sqrt[y/(x + y*I)]] |
Error | Failure | - | Failed [9 / 9]
{LessEqual[1.3862943611198906, Complex[0.5672499697282593, -1.7874177081206242]] <- {Rule[x, 1.5], Rule[y, 1.5]}LessEqual[1.3862943611198906, Complex[0.6277320470267476, -0.9602476282953896]] <- {Rule[x, 1.5], Rule[y, 0.5]} |
| 19.24.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{z}\CarlsonsymellintRF@{0}{y}{z}+\ln@@{\sqrt{y/z}} \leq \tfrac{1}{2}\pi} | sqrt(x + y*I)*0.5*int(1/(sqrt(t+0)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity)+ ln(sqrt(y/(x + y*I))) <= (1)/(2)*Pi |
Sqrt[x + y*I]*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0]+ Log[Sqrt[y/(x + y*I)]] <= Divide[1,2]*Pi |
Error | Failure | - | Failed [9 / 9]
{LessEqual[Complex[0.5672499697282593, -1.7874177081206242], 1.5707963267948966] <- {Rule[x, 1.5], Rule[y, 1.5]}LessEqual[Complex[0.6277320470267476, -0.9602476282953896], 1.5707963267948966] <- {Rule[x, 1.5], Rule[y, 0.5]} |
| 19.24.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2} \leq z^{-1/2}\CarlsonsymellintRG@{0}{y}{z}} | Error |
Divide[1,2] <= (x + y*I)^(- 1/ 2)* Sqrt[x + y*I-0]*(EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]+(Cot[ArcCos[Sqrt[0/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]+Cot[ArcCos[Sqrt[0/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/x + y*I]]]^2]) |
Missing Macro Error | Failure | - | Failed [9 / 9]
{LessEqual[0.5, Plus[Complex[1.0084590214609772, 0.7147093671486319], Times[Complex[0.2643318009908678, 0.8730286325904596], Power[Plus[1.0, Times[Complex[-1.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]] <- {Rule[x, 1.5], Rule[y, 1.5]}LessEqual[0.5, Plus[Complex[1.0897585107701309, 0.2919625251300463], Times[Complex[0.3515775842541431, 0.5688644810057831], Power[Plus[1.0, Times[Complex[-1.0, 0.5], Power[k, 2]]], Rational[1, 2]]]]] <- {Rule[x, 1.5], Rule[y, 0.5]} |
| 19.24.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z^{-1/2}\CarlsonsymellintRG@{0}{y}{z} \leq \tfrac{1}{4}\pi} | Error |
(x + y*I)^(- 1/ 2)* Sqrt[x + y*I-0]*(EllipticE[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]+(Cot[ArcCos[Sqrt[0/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]+Cot[ArcCos[Sqrt[0/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/x + y*I]]]^2]) <= Divide[1,4]*Pi |
Missing Macro Error | Failure | - | Failed [9 / 9]
{LessEqual[Plus[Complex[1.0084590214609772, 0.7147093671486319], Times[Complex[0.2643318009908678, 0.8730286325904596], Power[Plus[1.0, Times[Complex[-1.0, 1.5], Power[k, 2]]], Rational[1, 2]]]], 0.7853981633974483] <- {Rule[x, 1.5], Rule[y, 1.5]}LessEqual[Plus[Complex[1.0897585107701309, 0.2919625251300463], Times[Complex[0.3515775842541431, 0.5688644810057831], Power[Plus[1.0, Times[Complex[-1.0, 0.5], Power[k, 2]]], Rational[1, 2]]]], 0.7853981633974483] <- {Rule[x, 1.5], Rule[y, 0.5]} |
| 19.24.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{y^{3/2}+z^{3/2}}{2}\right)^{2/3} \leq \frac{4}{\pi}\CarlsonsymellintRG@{0}{y^{2}}{z^{2}}} | Error |
(Divide[(y)^(3/ 2)+(x + y*I)^(3/ 2),2])^(2/ 3) <= Divide[4,Pi]*Sqrt[(x + y*I)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(x + y*I)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-0)]+Cot[ArcCos[Sqrt[0/(x + y*I)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(x + y*I)^(2)]]]^2]) |
Missing Macro Error | Failure | - | Failed [9 / 9]
{LessEqual[Complex[1.4250443092558214, 0.7875512141675095], Complex[2.850438542245679, 1.5730146161508307]] <- {Rule[x, 1.5], Rule[y, 1.5]}LessEqual[Complex[1.0588191704631045, 0.29794136993360365], Complex[2.118851869395612, 0.5983245902184247]] <- {Rule[x, 1.5], Rule[y, 0.5]} |
| 19.24.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{4}{\pi}\CarlsonsymellintRG@{0}{y^{2}}{z^{2}} \leq \left(\frac{y^{2}+z^{2}}{2}\right)^{1/2}} | Error |
Divide[4,Pi]*Sqrt[(x + y*I)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(x + y*I)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(x + y*I)^(2)]],((x + y*I)^(2)-(y)^(2))/((x + y*I)^(2)-0)]+Cot[ArcCos[Sqrt[0/(x + y*I)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(x + y*I)^(2)]]]^2]) <= (Divide[(y)^(2)+(x + y*I)^(2),2])^(1/ 2) |
Missing Macro Error | Failure | - | Failed [9 / 9]
{LessEqual[Complex[2.850438542245679, 1.5730146161508307], Complex[1.3491805799609005, 0.8338394553771318]] <- {Rule[x, 1.5], Rule[y, 1.5]}LessEqual[Complex[2.118851869395612, 0.5983245902184247], Complex[1.112897508375995, 0.3369582528288897]] <- {Rule[x, 1.5], Rule[y, 0.5]} |
| 19.24.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\sqrt{p}}(2yz+yp+zp)^{-1/2} \leq \frac{4}{3\pi}\CarlsonsymellintRJ@{0}{y}{z}{p}} | Error |
Divide[2,Sqrt[p]]*(2*y*(x + y*I)+ y*p +(x + y*I)*p)^(- 1/ 2) <= Divide[4,3*Pi]*3*(x + y*I-0)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-0),ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/Sqrt[x + y*I-0] |
Missing Macro Error | Failure | - | Failed [180 / 180]
{LessEqual[Complex[0.13508456755677706, -1.1829936015765863], Complex[-0.3213270063391195, -0.3051912044731223]] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[0.7797231369520263, -0.6247258696161743], Complex[-0.6706782382611747, 0.54526856836685]] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{4}{3\pi}\CarlsonsymellintRJ@{0}{y}{z}{p} \leq (yzp^{2})^{-3/8}} | Error |
Divide[4,3*Pi]*3*(x + y*I-0)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-0),ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]-EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)])/Sqrt[x + y*I-0] <= (y*(x + y*I)*(p)^(2))^(- 3/ 8) |
Missing Macro Error | Failure | - | Failed [180 / 180]
{LessEqual[Complex[-0.3213270063391195, -0.3051912044731223], Complex[0.5136265917030035, 0.9609277658721954]] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[-0.6706782382611747, 0.54526856836685], Complex[0.8422602311268256, -0.6912251080442312]] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{a_{n}} \leq \frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}}} | (1)/(a[n]) 0.5*int(1/(sqrt(t+0)*sqrt(t+a(a[0])^(2))*sqrt(t+g(g[0])^(2))), t = 0..infinity) |
Divide[1,Subscript[a, n]] EllipticF[ArcCos[Sqrt[0/g(Subscript[g, 0])^(2)]],(g(Subscript[g, 0])^(2)-a(Subscript[a, 0])^(2))/(g(Subscript[g, 0])^(2)-0)]/Sqrt[g(Subscript[g, 0])^(2)-0] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300] {LessEqual[Complex[1.7320508075688774, -0.9999999999999999], Times[2.0, Power[Times[Complex[0.5000000000000001, 0.8660254037844386], g], Rational[-1, 2]], EllipticK[Times[Complex[2.0000000000000004, -3.4641016151377544], Plus[Times[Complex[-0.12500000000000003, -0.21650635094610965], a], Times[Complex[0.12500000000000003, 0.21650635094610965], g]], Power[g, -1]]]]] <- {Rule[n, 3], Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, n], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}LessEqual[Complex[1.7320508075688774, -0.9999999999999999], Times[2.0, Power[Times[Complex[-0.4999999999999998, -0.8660254037844387], g], Rational[-1, 2]], EllipticK[Times[Complex[-1.9999999999999991, 3.464101615137755], Plus[Times[Complex[-0.12500000000000003, -0.21650635094610965], a], Times[Complex[-0.124
|
| 19.24.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2}{\pi}\CarlsonsymellintRF@{0}{a_{0}^{2}}{g_{0}^{2}} \leq \frac{1}{g_{n}}} | 0.5*int(1/(sqrt(t+0)*sqrt(t+a(a[0])^(2))*sqrt(t+g(g[0])^(2))), t = 0..infinity) <= (1)/(g[n]) |
EllipticF[ArcCos[Sqrt[0/g(Subscript[g, 0])^(2)]],(g(Subscript[g, 0])^(2)-a(Subscript[a, 0])^(2))/(g(Subscript[g, 0])^(2)-0)]/Sqrt[g(Subscript[g, 0])^(2)-0] <= Divide[1,Subscript[g, n]] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300] {LessEqual[Times[2.0, Power[Times[Complex[0.5000000000000001, 0.8660254037844386], g], Rational[-1, 2]], EllipticK[Times[Complex[2.0000000000000004, -3.4641016151377544], Plus[Times[Complex[-0.12500000000000003, -0.21650635094610965], a], Times[Complex[0.12500000000000003, 0.21650635094610965], g]], Power[g, -1]]]], Complex[1.7320508075688774, -0.9999999999999999]] <- {Rule[n, 3], Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, n], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}LessEqual[Times[2.0, Power[Times[Complex[0.5000000000000001, 0.8660254037844386], g], Rational[-1, 2]], EllipticK[Times[Complex[2.0000000000000004, -3.4641016151377544], Plus[Times[Complex[-0.12500000000000003, -0.21650635094610965], a], Times[Complex[0.12500000000000003, 0.21650635094610965], g]], Power[g,
|
| 19.24#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{n+1} = (a_{n}+g_{n})/2} | a[n + 1] = (a[n]+ g[n])/ 2 |
Subscript[a, n + 1] == (Subscript[a, n]+ Subscript[g, n])/ 2 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.24#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g_{n+1} = \sqrt{a_{n}g_{n}}} | g[n + 1] = sqrt(a[n]*g[n]) |
Subscript[g, n + 1] == Sqrt[Subscript[a, n]*Subscript[g, n]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.24.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L(a,b) = 8\CarlsonsymellintRG@{0}{a^{2}}{b^{2}}} | Error |
L*(a , b) == 8*Sqrt[(b)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(b)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+Cot[ArcCos[Sqrt[0/(b)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(b)^(2)]]]^2]) |
Missing Macro Error | Failure | - | Error |
| 19.24#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{0}\CarlsonsymellintRG@{x}{y}{0} > \tfrac{1}{8}\pi^{2}} | Error |
EllipticF[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]/Sqrt[0-x]*Sqrt[0-x]*(EllipticE[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]+(Cot[ArcCos[Sqrt[x/0]]])^2*EllipticF[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]+Cot[ArcCos[Sqrt[x/0]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/0]]]^2]) > Divide[1,8]*(Pi)^(2) |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Greater[Indeterminate, 1.2337005501361697] <- {Rule[x, 1.5], Rule[y, -1.5]}Greater[Indeterminate, 1.2337005501361697] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{0}+2\CarlsonsymellintRG@{x}{y}{0} > \pi} | Error |
EllipticF[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]/Sqrt[0-x]+ 2*Sqrt[0-x]*(EllipticE[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]+(Cot[ArcCos[Sqrt[x/0]]])^2*EllipticF[ArcCos[Sqrt[x/0]],(0-y)/(0-x)]+Cot[ArcCos[Sqrt[x/0]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/0]]]^2]) > Pi |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Greater[Indeterminate, 3.141592653589793] <- {Rule[x, 1.5], Rule[y, -1.5]}Greater[Indeterminate, 3.141592653589793] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{2}\,g_{1}^{2} \leq \frac{\CarlsonsymellintRG@{a_{0}^{2}}{g_{0}^{2}}{0}}{\CarlsonsymellintRF@{a_{0}^{2}}{g_{0}^{2}}{0}}} | Error |
Divide[Sqrt[0-a(Subscript[a, 0])^(2)]*(EllipticE[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]],(0-g(Subscript[g, 0])^(2))/(0-a(Subscript[a, 0])^(2))]+(Cot[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]]])^2*EllipticF[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]],(0-g(Subscript[g, 0])^(2))/(0-a(Subscript[a, 0])^(2))]+Cot[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]]]^2]),EllipticF[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]],(0-g(Subscript[g, 0])^(2))/(0-a(Subscript[a, 0])^(2))]/Sqrt[0-a(Subscript[a, 0])^(2)]] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{LessEqual[Complex[0.06250000000000001, 0.10825317547305482], Indeterminate] <- {Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}LessEqual[Complex[-0.06249999999999997, -0.10825317547305484], Indeterminate] <- {Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.24.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\CarlsonsymellintRG@{a_{0}^{2}}{g_{0}^{2}}{0}}{\CarlsonsymellintRF@{a_{0}^{2}}{g_{0}^{2}}{0}} \leq \frac{1}{2}\,a_{1}^{2}} | Error |
Divide[Sqrt[0-a(Subscript[a, 0])^(2)]*(EllipticE[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]],(0-g(Subscript[g, 0])^(2))/(0-a(Subscript[a, 0])^(2))]+(Cot[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]]])^2*EllipticF[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]],(0-g(Subscript[g, 0])^(2))/(0-a(Subscript[a, 0])^(2))]+Cot[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]]]^2]),EllipticF[ArcCos[Sqrt[a(Subscript[a, 0])^(2)/0]],(0-g(Subscript[g, 0])^(2))/(0-a(Subscript[a, 0])^(2))]/Sqrt[0-a(Subscript[a, 0])^(2)]] <= Divide[1,2]*(Subscript[a, 1])^(2) |
Missing Macro Error | Failure | - | Failed [300 / 300]
{LessEqual[Indeterminate, Complex[0.06250000000000001, 0.10825317547305482]] <- {Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}LessEqual[Indeterminate, Complex[0.06250000000000001, 0.10825317547305482]] <- {Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[g, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.24.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{3}{\sqrt{x}+\sqrt{y}+\sqrt{z}} \leq \CarlsonsymellintRF@{x}{y}{z}} | (3)/(sqrt(x)+sqrt(y)+sqrt(x + y*I)) <= 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) |
Divide[3,Sqrt[x]+Sqrt[y]+Sqrt[x + y*I]] <= EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] |
Aborted | Failure | Error | Failed [18 / 18]
{LessEqual[Complex[1.0934408788539995, -0.2839050517129825], Complex[-0.16214470973156064, 0.6784437678906974]] <- {Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[0.7738030002696183, -0.11364498174072818], Complex[-0.28823404661462, -0.7809212115368181]] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{z} \leq \frac{1}{(xyz)^{1/6}}} | 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) <= (1)/((x*y*(x + y*I))^(1/ 6)) |
EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] <= Divide[1,(x*y*(x + y*I))^(1/ 6)] |
Aborted | Failure | Error | Failed [18 / 18]
{LessEqual[Complex[-0.16214470973156064, 0.6784437678906974], Complex[0.7120063770987297, -0.29492269789042613]] <- {Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[-0.28823404661462, -0.7809212115368181], Complex[0.7640769591692358, -0.10059264002361257]] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\frac{5}{\sqrt{x}+\sqrt{y}+\sqrt{z}+2\sqrt{p}}\right)^{3} \leq \CarlsonsymellintRJ@{x}{y}{z}{p}} | Error |
(Divide[5,Sqrt[x]+Sqrt[y]+Sqrt[x + y*I]+ 2*Sqrt[p]])^(3) <= 3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] |
Missing Macro Error | Failure | - | Failed [180 / 180]
{LessEqual[Complex[1.3310335634294785, -1.2911719373315522], Complex[-0.2876927312707393, -0.327259429717868]] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[0.7477899794343462, -0.4392695700678081], Complex[-0.36602768453446033, 0.5058947820270108]] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{x}{y}{z}{p} \leq (xyzp^{2})^{-3/10}} | Error |
3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] <= (x*y*(x + y*I)*(p)^(2))^(- 3/ 10) |
Missing Macro Error | Failure | - | Failed [180 / 180]
{LessEqual[Complex[-0.2876927312707393, -0.327259429717868], Complex[0.6159220908806466, 0.7211521128667333]] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[-0.36602768453446033, 0.5058947820270108], Complex[0.8086249764673956, -0.49552602288885395]] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{3}(\sqrt{x}+\sqrt{y}+\sqrt{z}) \leq \CarlsonsymellintRG@{x}{y}{z}} | Error |
Divide[1,3]*(Sqrt[x]+Sqrt[y]+Sqrt[x + y*I]) <= Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) |
Missing Macro Error | Failure | - | Failed [18 / 18]
{LessEqual[Complex[0.8567842015469013, 0.22245863288189585], Times[Complex[0.8660254037844386, -0.8660254037844385], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[1.2650324920107643, 0.1857896575819671], Times[Complex[0.8660254037844386, 0.8660254037844385], Plus[Complex[1.0566228789425183, 0.3443432776585209], Times[Complex[0.3176872874027722, 1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{z}\CarlsonsymellintRG@{x}{y}{z} > 1} | Error |
EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x]*Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) > 1 |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Greater[Times[Complex[0.44712810031579164, 0.7279709757493625], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]], 1.0] <- {Rule[x, 1.5], Rule[y, -1.5]}Greater[Times[Complex[0.42667960094115687, -0.925915614148855], Plus[Complex[1.0566228789425183, 0.3443432776585209], Times[Complex[0.3176872874027722, 1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]], 1.0] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{z}+\CarlsonsymellintRG@{x}{y}{z} > 2} | Error |
EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x]+ Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) > 2 |
Missing Macro Error | Failure | - | Failed [18 / 18]
{Greater[Plus[Complex[-0.16214470973156064, 0.6784437678906974], Times[Complex[0.8660254037844386, -0.8660254037844385], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]]], 2.0] <- {Rule[x, 1.5], Rule[y, -1.5]}Greater[Plus[Complex[-0.28823404661462, -0.7809212115368181], Times[Complex[0.8660254037844386, 0.8660254037844385], Plus[Complex[1.0566228789425183, 0.3443432776585209], Times[Complex[0.3176872874027722, 1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, 1.5], Power[k, 2]]], Rational[1, 2]]]]]], 2.0] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x}{\tfrac{1}{2}(y+z)} \leq \CarlsonsymellintRF@{x}{y}{z}} | Error |
1/Sqrt[Divide[1,2]*(y +(x + y*I))]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(Divide[1,2]*(y +(x + y*I)))] <= EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] |
Missing Macro Error | Failure | - | Failed [18 / 18]
{LessEqual[Complex[0.9580693887321644, 0.49152363500125495], Complex[-0.16214470973156064, 0.6784437678906974]] <- {Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[0.7805167095081702, -0.12346643314922054], Complex[-0.28823404661462, -0.7809212115368181]] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.24.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{z} \leq \CarlsonellintRC@{x}{\sqrt{yz}}} | Error |
EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] <= 1/Sqrt[Sqrt[y*(x + y*I)]]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(Sqrt[y*(x + y*I)])] |
Missing Macro Error | Failure | - | Failed [18 / 18]
{LessEqual[Complex[-0.16214470973156064, 0.6784437678906974], Complex[0.7308447207533646, -0.31118718328917466]] <- {Rule[x, 1.5], Rule[y, -1.5]}LessEqual[Complex[-0.28823404661462, -0.7809212115368181], Complex[0.765857524311696, -0.1031964554328576]] <- {Rule[x, 1.5], Rule[y, 1.5]} |
| 19.25#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = \CarlsonsymellintRF@{0}{{k^{\prime}}^{2}}{1}} | EllipticK(k) = 0.5*int(1/(sqrt(t+0)*sqrt(t+1 - (k)^(2))*sqrt(t+1)), t = 0..infinity) |
EllipticK[(k)^2] == EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]/Sqrt[1-0] |
Failure | Failure | Error | Failed [3 / 3]
{DirectedInfinity[] <- {Rule[k, 1]}Complex[-0.16657773258291342, -1.0782578237498217] <- {Rule[k, 2]} |
| 19.25#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{k} = 2\CarlsonsymellintRG@{0}{{k^{\prime}}^{2}}{1}} | Error |
EllipticE[(k)^2] == 2*Sqrt[1-0]*(EllipticE[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2*EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2]) |
Missing Macro Error | Failure | - | Failed [3 / 3]
{-2.820197789027711 <- {Rule[k, 1]}Complex[-4.864068276731299, 1.343854231387098] <- {Rule[k, 2]} |
| 19.25#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{k} = \tfrac{1}{3}{k^{\prime}}^{2}\left(\CarlsonsymellintRD@{0}{{k^{\prime}}^{2}}{1}+\CarlsonsymellintRD@{0}{1}{{k^{\prime}}^{2}}\right)} | Error |
EllipticE[(k)^2] == Divide[1,3]*1 - (k)^(2)*(3*(EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]-EllipticE[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)])/((1-1 - (k)^(2))*(1-0)^(1/2))+ 3*(EllipticF[ArcCos[Sqrt[0/1 - (k)^(2)]],(1 - (k)^(2)-1)/(1 - (k)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/1 - (k)^(2)]],(1 - (k)^(2)-1)/(1 - (k)^(2)-0)])/((1 - (k)^(2)-1)*(1 - (k)^(2)-0)^(1/2))) |
Missing Macro Error | Failure | - | Failed [3 / 3]
{DirectedInfinity[] <- {Rule[k, 1]}Complex[7.885081986624734, -2.293856789051463] <- {Rule[k, 2]} |
| 19.25#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k}-\compellintEk@{k} = k^{2}\compellintDk@{k}} | EllipticK(k)- EllipticE(k) = (k)^(2)* (EllipticK(k) - EllipticE(k))/(k)^2 |
EllipticK[(k)^2]- EllipticE[(k)^2] == (k)^(2)* Divide[EllipticK[(k)^2] - EllipticE[(k)^2], (k)^4] |
Successful | Failure | - | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]}Complex[0.3274322182097533, -1.81658404135269] <- {Rule[k, 2]} |
| 19.25#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2}\compellintDk@{k} = \tfrac{1}{3}k^{2}\CarlsonsymellintRD@{0}{{k^{\prime}}^{2}}{1}} | Error |
(k)^(2)* Divide[EllipticK[(k)^2] - EllipticE[(k)^2], (k)^4] == Divide[1,3]*(k)^(2)* 3*(EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]-EllipticE[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)])/((1-1 - (k)^(2))*(1-0)^(1/2)) |
Missing Macro Error | Failure | - | Failed [3 / 3]
{DirectedInfinity[] <- {Rule[k, 1]}Complex[-1.5165865988698335, -0.6055280137842299] <- {Rule[k, 2]} |
| 19.25#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintEk@{k}-{k^{\prime}}^{2}\compellintKk@{k} = \tfrac{1}{3}k^{2}{k^{\prime}}^{2}\CarlsonsymellintRD@{0}{1}{{k^{\prime}}^{2}}} | Error |
EllipticE[(k)^2]-1 - (k)^(2)*EllipticK[(k)^2] == Divide[1,3]*(k)^(2)*1 - (k)^(2)*3*(EllipticF[ArcCos[Sqrt[0/1 - (k)^(2)]],(1 - (k)^(2)-1)/(1 - (k)^(2)-0)]-EllipticE[ArcCos[Sqrt[0/1 - (k)^(2)]],(1 - (k)^(2)-1)/(1 - (k)^(2)-0)])/((1 - (k)^(2)-1)*(1 - (k)^(2)-0)^(1/2)) |
Missing Macro Error | Failure | - | Failed [3 / 3]
{Indeterminate <- {Rule[k, 1]}Complex[-2.3636107378197124, 2.0191745059478237] <- {Rule[k, 2]} |
| 19.25.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintPik@{\alpha^{2}}{k}-\compellintKk@{k} = \tfrac{1}{3}\alpha^{2}\CarlsonsymellintRJ@{0}{{k^{\prime}}^{2}}{1}{1-\alpha^{2}}} | Error |
EllipticPi[\[Alpha]^(2), (k)^2]- EllipticK[(k)^2] == Divide[1,3]*\[Alpha]^(2)* 3*(1-0)/(1-1 - \[Alpha]^(2))*(EllipticPi[(1-1 - \[Alpha]^(2))/(1-0),ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]-EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)])/Sqrt[1-0] |
Missing Macro Error | Failure | - | Failed [9 / 9]
{Indeterminate <- {Rule[k, 1], Rule[α, 1.5]}Complex[-1.5241433161083033, 0.5547659663605348] <- {Rule[k, 2], Rule[α, 1.5]} |
| 19.25.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintPik@{\alpha^{2}}{k} = -\tfrac{1}{3}(k^{2}/\alpha^{2})\CarlsonsymellintRJ@{0}{1-k^{2}}{1}{1-(k^{2}/\alpha^{2})}} | Error |
EllipticPi[\[Alpha]^(2), (k)^2] == -Divide[1,3]*((k)^(2)/ \[Alpha]^(2))* 3*(1-0)/(1-1 -((k)^(2)/ \[Alpha]^(2)))*(EllipticPi[(1-1 -((k)^(2)/ \[Alpha]^(2)))/(1-0),ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)]-EllipticF[ArcCos[Sqrt[0/1]],(1-1 - (k)^(2))/(1-0)])/Sqrt[1-0] |
Missing Macro Error | Failure | - | Skip - No test values generated |
| 19.25.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{k} = \CarlsonsymellintRF@{c-1}{c-k^{2}}{c}} | EllipticF(sin(phi), k) = 0.5*int(1/(sqrt(t+c - 1)*sqrt(t+c - (k)^(2))*sqrt(t+c)), t = 0..infinity) |
EllipticF[\[Phi], (k)^2] == EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1] |
Failure | Failure | Failed [180 / 180] 180/180]: [[Float(undefined)+Float(undefined)*I <- {c = -3/2, phi = 1/2*3^(1/2)+1/2*I, k = 1}3.854689052+3.461698034*I <- {c = -3/2, phi = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [180 / 180]
{Complex[2.0026000841930385, 1.2187088711714384] <- {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.4748265293714395, 0.7583435972865697] <- {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\incellintFk@{\phi}{k}}{k} = \tfrac{1}{3}k\CarlsonsymellintRD@{c-1}{c}{c-k^{2}}} | Error |
D[EllipticF[\[Phi], (k)^2], k] == Divide[1,3]*k*3*(EllipticF[ArcCos[Sqrt[c - 1/c - (k)^(2)]],(c - (k)^(2)-c)/(c - (k)^(2)-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c - (k)^(2)]],(c - (k)^(2)-c)/(c - (k)^(2)-c - 1)])/((c - (k)^(2)-c)*(c - (k)^(2)-c - 1)^(1/2)) |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Indeterminate <- {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.4045300788217367, 0.4404710702025501] <- {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} = 2\CarlsonsymellintRG@{c-1}{c-k^{2}}{c}-(c-1)\CarlsonsymellintRF@{c-1}{c-k^{2}}{c}-\sqrt{(c-1)(c-k^{2})/c}} | Error |
EllipticE[\[Phi], (k)^2] == 2*Sqrt[c-c - 1]*(EllipticE[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]+(Cot[ArcCos[Sqrt[c - 1/c]]])^2*EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]+Cot[ArcCos[Sqrt[c - 1/c]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[c - 1/c]]]^2])-(c - 1)* EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1]-Sqrt[(c - 1)*(c - (k)^(2))/ c] |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Complex[5.787775994567906, 4.022803158659452] <- {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[6.805668366738806, 3.968311704298834] <- {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} = \CarlsonsymellintRF@{c-1}{c-k^{2}}{c}-\tfrac{1}{3}k^{2}\CarlsonsymellintRD@{c-1}{c-k^{2}}{c}} | Error |
EllipticE[\[Phi], (k)^2] == EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1]-Divide[1,3]*(k)^(2)* 3*(EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/((c-c - (k)^(2))*(c-c - 1)^(1/2)) |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Complex[3.5743811704478246, 0.7698502565730785] <- {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[3.9424508382496875, -1.017653751864599] <- {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} = {k^{\prime}}^{2}\CarlsonsymellintRF@{c-1}{c-k^{2}}{c}+\tfrac{1}{3}k^{2}{k^{\prime}}^{2}\CarlsonsymellintRD@{c-1}{c}{c-k^{2}}+k^{2}\sqrt{(c-1)/(c(c-k^{2}))}} | Error |
EllipticE[\[Phi], (k)^2] == 1 - (k)^(2)*EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1]+Divide[1,3]*(k)^(2)*1 - (k)^(2)*3*(EllipticF[ArcCos[Sqrt[c - 1/c - (k)^(2)]],(c - (k)^(2)-c)/(c - (k)^(2)-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c - (k)^(2)]],(c - (k)^(2)-c)/(c - (k)^(2)-c - 1)])/((c - (k)^(2)-c)*(c - (k)^(2)-c - 1)^(1/2))+ (k)^(2)*Sqrt[(c - 1)/(c*(c - (k)^(2)))] |
Missing Macro Error | Failure | - | Failed [20 / 20]
{Complex[-1.0687219916023158, 0.8637282710955538] <- {Rule[c, 1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.7724732696890155, 1.0672164584507502] <- {Rule[c, 1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.25.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} = -\tfrac{1}{3}{k^{\prime}}^{2}\CarlsonsymellintRD@{c-k^{2}}{c}{c-1}+\sqrt{(c-k^{2})/(c(c-1))}} | Error |
EllipticE[\[Phi], (k)^2] == -Divide[1,3]*1 - (k)^(2)*3*(EllipticF[ArcCos[Sqrt[c - (k)^(2)/c - 1]],(c - 1-c)/(c - 1-c - (k)^(2))]-EllipticE[ArcCos[Sqrt[c - (k)^(2)/c - 1]],(c - 1-c)/(c - 1-c - (k)^(2))])/((c - 1-c)*(c - 1-c - (k)^(2))^(1/2))+Sqrt[(c - (k)^(2))/(c*(c - 1))] |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Complex[3.6312701919621486, -1.3602272606820804] <- {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.7754142926962797, -0.6029933704091625] <- {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{\incellintEk@{\phi}{k}}{k} = -\tfrac{1}{3}k\CarlsonsymellintRD@{c-1}{c-k^{2}}{c}} | Error |
D[EllipticE[\[Phi], (k)^2], k] == -Divide[1,3]*k*3*(EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/((c-c - (k)^(2))*(c-c - 1)^(1/2)) |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Complex[1.571781086254786, -0.44885861459835996] <- {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.233812154439124, -0.8879986745755843] <- {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintDk@{\phi}{k} = \tfrac{1}{3}\CarlsonsymellintRD@{c-1}{c-k^{2}}{c}} | Error |
Divide[EllipticF[\[Phi], (k)^2] - EllipticE[\[Phi], (k)^2], (k)^4] == Divide[1,3]*3*(EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/((c-c - (k)^(2))*(c-c - 1)^(1/2)) |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Complex[-1.571781086254786, 0.44885861459835996] <- {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.6083725296430629, 0.41279951787826946] <- {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{\alpha^{2}}{k}-\incellintFk@{\phi}{k} = \tfrac{1}{3}\alpha^{2}\CarlsonsymellintRJ@{c-1}{c-k^{2}}{c}{c-\alpha^{2}}} | Error |
EllipticPi[\[Alpha]^(2), \[Phi],(k)^2]- EllipticF[\[Phi], (k)^2] == Divide[1,3]*\[Alpha]^(2)* 3*(c-c - 1)/(c-c - \[Alpha]^(2))*(EllipticPi[(c-c - \[Alpha]^(2))/(c-c - 1),ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/Sqrt[c-c - 1] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Complex[-0.9803588804354156, -0.9579910370435353] <- {Rule[c, -1.5], Rule[k, 1], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.6164275583611891, -0.384238714210872] <- {Rule[c, -1.5], Rule[k, 2], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintPik@{\phi}{\alpha^{2}}{k} = -\tfrac{1}{3}\omega^{2}\CarlsonsymellintRJ@{c-1}{c-k^{2}}{c}{c-\omega^{2}}+\sqrt{\frac{(c-1)(c-k^{2})}{(\alpha^{2}-1)(1-\omega^{2})}}\*\CarlsonellintRC@{c(\alpha^{2}-1)(1-\omega^{2})}{(\alpha^{2}-c)(c-\omega^{2})}} | Error |
EllipticPi[\[Alpha]^(2), \[Phi],(k)^2] == -Divide[1,3]*\[Omega]^(2)* 3*(c-c - 1)/(c-c - \[Omega]^(2))*(EllipticPi[(c-c - \[Omega]^(2))/(c-c - 1),ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/Sqrt[c-c - 1]+Sqrt[Divide[(c - 1)*(c - (k)^(2)),(\[Alpha]^(2)- 1)*(1 - \[Omega]^(2))]]* 1/Sqrt[(\[Alpha]^(2)- c)*(c - \[Omega]^(2))]*Hypergeometric2F1[1/2,1/2,3/2,1-(c*(\[Alpha]^(2)- 1)*(1 - \[Omega]^(2)))/((\[Alpha]^(2)- c)*(c - \[Omega]^(2)))] |
Missing Macro Error | Aborted | - | Failed [300 / 300]
{Complex[-0.11631142199526823, 0.9703799109463437] <- {Rule[c, -1.5], Rule[k, 3], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ω, -2]}Complex[-0.11631142199526823, 0.9703799109463437] <- {Rule[c, -1.5], Rule[k, 3], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ω, 2]} |
| 19.25.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintFk@{\phi}{k} = \CarlsonsymellintRF@{x}{y}{z}} | EllipticF(sin(phi), k) = 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) |
EllipticF[\[Phi], (k)^2] == EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] |
Aborted | Failure | Failed [300 / 300] 300/300]: [[2.547570015-.6488873983*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, k = 1}2.209888328-.6080126261*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, k = 2} |
Failed [300 / 300]
{Complex[0.5939484671297026, -0.40701440305540804] <- {Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.5587134153531784, -0.34669285510288844] <- {Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (x,y,z) = (c-1,c-k^{2},c)} | (x , y ,(x + y*I)) = (c - 1 , c - (k)^(2), c) |
(x , y ,(x + y*I)) == (c - 1 , c - (k)^(2), c) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.25#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \phi = \acos@@{\sqrt{\ifrac{x}{z}}}} | phi = arccos(sqrt((x)/(x + y*I))) |
\[Phi] == ArcCos[Sqrt[Divide[x,x + y*I]]] |
Failure | Failure | Failed [180 / 180] 180/180]: [[.806272406e-1+.9406867936*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2}.806272406e-1+.593132064e-1*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = 3/2} |
Failed [180 / 180]
{Complex[-0.35238546150522904, 0.6906867935097715] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.0353981633974483, 0.8736994954019909] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.25#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \acos@@{\sqrt{\ifrac{x}{z}}} = \asin@@{\sqrt{\ifrac{(z-x)}{z}}}} | arccos(sqrt((x)/(x + y*I))) = arcsin(sqrt(((x + y*I)- x)/(x + y*I))) |
ArcCos[Sqrt[Divide[x,x + y*I]]] == ArcSin[Sqrt[Divide[(x + y*I)- x,x + y*I]]] |
Failure | Failure | Successful [Tested: 18] | Successful [Tested: 18] |
| 19.25#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k = \sqrt{\frac{z-y}{z-x}}} | k = sqrt(((x + y*I)- y)/((x + y*I)- x)) |
k == Sqrt[Divide[(x + y*I)- y,(x + y*I)- x]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.25#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha^{2} = \frac{z-p}{z-x}} | (alpha)^(2) = ((x + y*I)- p)/((x + y*I)- x) |
\[Alpha]^(2) == Divide[(x + y*I)- p,(x + y*I)- x] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.25.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z-x)^{1/2}\CarlsonsymellintRF@{x}{y}{z} = \incellintFk@{\phi}{k}} | ((x + y*I)- x)^(1/ 2)* 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) = EllipticF(sin(phi), k) |
((x + y*I)- x)^(1/ 2)* EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] == EllipticF[\[Phi], (k)^2] |
Aborted | Failure | Failed [300 / 300] 300/300]: [[-1.167656510+1.966567574*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, k = 1}-.8299748231+1.925692802*I <- {phi = 1/2*3^(1/2)+1/2*I, x = 3/2, y = -3/2, k = 2} |
Failed [300 / 300]
{Complex[0.015324342917649614, 0.4565416109140732] <- {Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.050559394694173865, 0.3962200629615536] <- {Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z-x)^{3/2}\CarlsonsymellintRD@{x}{y}{z} = (3/k^{2})(\incellintFk@{\phi}{k}-\incellintEk@{\phi}{k})} | Error |
((x + y*I)- x)^(3/ 2)* 3*(EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/((x + y*I-y)*(x + y*I-x)^(1/2)) == (3/ (k)^(2))*(EllipticF[\[Phi], (k)^2]- EllipticE[\[Phi], (k)^2]) |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Complex[-0.9041684186949032, 0.18989946051507803] <- {Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.8729885067685752, 0.19149534336253457] <- {Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (z-x)^{3/2}\CarlsonsymellintRJ@{x}{y}{z}{p} = (3/\alpha^{2}){(\incellintPik@{\phi}{\alpha^{2}}{k}-\incellintFk@{\phi}{k})}} | Error |
((x + y*I)- x)^(3/ 2)* 3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] == (3/ \[Alpha]^(2))*(EllipticPi[\[Alpha]^(2), \[Phi],(k)^2]- EllipticF[\[Phi], (k)^2]) |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Complex[-8.905365206673954*^-4, 0.6653826564189609] <- {Rule[k, 1], Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.030816807002235325, 0.6810951786851601] <- {Rule[k, 2], Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2(z-x)^{-1/2}\CarlsonsymellintRG@{x}{y}{z} = \incellintEk@{\phi}{k}+(\cot@@{\phi})^{2}\incellintFk@{\phi}{k}+(\cot@@{\phi})\sqrt{1-k^{2}\sin^{2}@@{\phi}}} | Error |
2*((x + y*I)- x)^(- 1/ 2)* Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) == EllipticE[\[Phi], (k)^2]+(Cot[\[Phi]])^(2)* EllipticF[\[Phi], (k)^2]+(Cot[\[Phi]])*Sqrt[1 - (k)^(2)* (Sin[\[Phi]])^(2)] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Complex[-1.8997799949200251, -0.4031557744461449] <- {Rule[k, 1], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-3.0701379688219372, -2.1411109504853227] <- {Rule[k, 2], Rule[x, 1.5], Rule[y, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.25#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Delta(\mathrm{n,d}) = k^{2}} | Delta*(n , d) = (k)^(2) |
\[CapitalDelta]*(n , d) == (k)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.25#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Delta(\mathrm{d,c}) = {k^{\prime}}^{2}} | Delta*(d , c) = 1 - (k)^(2) |
\[CapitalDelta]*(d , c) == 1 - (k)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.25#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Delta(\mathrm{n,c}) = 1} | Delta*(n , c) = 1 |
\[CapitalDelta]*(n , c) == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.25.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobiamk@{u}{k} = \CarlsonellintRC@{\Jacobiellcsk^{2}@{u}{k}}{\Jacobiellnsk^{2}@{u}{k}}} | Error |
JacobiAmplitude[u, Power[k, 2]] == 1/Sqrt[(JacobiNS[u, (k)^2])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((JacobiCS[u, (k)^2])^(2))/((JacobiNS[u, (k)^2])^(2))] |
Missing Macro Error | Aborted | - | Failed [18 / 30]
{Complex[-0.5428587296705786, 0.8636075147962846] <- {Rule[k, 1], Rule[u, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]}Complex[-0.6732377468613371, 0.8494366739388763] <- {Rule[k, 2], Rule[u, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.25.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle u = \CarlsonsymellintRF@{\genJacobiellk{p}{s}^{2}@{u}{k}}{\genJacobiellk{q}{s}^{2}@{u}{k}}{\genJacobiellk{r}{s}^{2}@{u}{k}}} | u = 0.5*int(1/(sqrt(t+genJacobiellk(p)*(s)^(2)* u*k)*sqrt(t+genJacobiellk(q)*(s)^(2)* u*k)*sqrt(t+genJacobiellk(r)*(s)^(2)* u*k)), t = 0..infinity) |
u == EllipticF[ArcCos[Sqrt[genJacobiellk(p)*(s)^(2)* u*k/genJacobiellk(r)*(s)^(2)* u*k]],(genJacobiellk(r)*(s)^(2)* u*k-genJacobiellk(q)*(s)^(2)* u*k)/(genJacobiellk(r)*(s)^(2)* u*k-genJacobiellk(p)*(s)^(2)* u*k)]/Sqrt[genJacobiellk(r)*(s)^(2)* u*k-genJacobiellk(p)*(s)^(2)* u*k] |
Aborted | Failure | Error | Failed [300 / 300] {Plus[Complex[0.43301270189221935, 0.24999999999999997], Times[Complex[-0.78471422644353, -0.9906313764027224], Power[Times[Complex[-1.7426678688862403, -1.3308892896287465], genJacobiellk], Rational[-1, 2]]]] <- {Rule[k, 1], Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[r, -1.5], Rule[s, -1.5], Rule[u, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Plus[Complex[0.43301270189221935, 0.24999999999999997], Times[Complex[-0.3766936106342851, -1.225388931598258], Power[Times[Complex[-3.4853357377724805, -2.661778579257493], genJacobiellk], Rational[-1, 2]]]] <- {Rule[k, 2], Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[r, -1.5], Rule[s, -1.5], Rule[u, Times[Rational[1, 2], Power[E, Times[Complex[0, Ration
|
| 19.26.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x+\lambda}{y+\lambda}{z+\lambda}+\CarlsonsymellintRF@{x+\mu}{y+\mu}{z+\mu} = \CarlsonsymellintRF@{x}{y}{z}} | 0.5*int(1/(sqrt(t+x + lambda)*sqrt(t+y + lambda)*sqrt(t+(x + y*I)+ lambda)), t = 0..infinity)+ 0.5*int(1/(sqrt(t+x + mu)*sqrt(t+y + mu)*sqrt(t+(x + y*I)+ mu)), t = 0..infinity) = 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]/Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]]+ EllipticF[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu])]/Sqrt[(x + y*I)+ \[Mu]-x + \[Mu]] == EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Complex[0.6992255245511445, -1.8246422705609677] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.2162365888422955, -0.7585970772170993] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.26.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x+\mu = \lambda^{-2}\left(\sqrt{(x+\lambda)yz}+\sqrt{x(y+\lambda)(z+\lambda)}\right)^{2}} | x + mu = (lambda)^(- 2)*(sqrt((x + lambda)* y*(x + y*I))+sqrt(x*(y + lambda)*((x + y*I)+ lambda)))^(2) |
x + \[Mu] == \[Lambda]^(- 2)*(Sqrt[(x + \[Lambda])* y*(x + y*I)]+Sqrt[x*(y + \[Lambda])*((x + y*I)+ \[Lambda])])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\xi,\eta,\zeta) = (x+\lambda,y+\lambda,z+\lambda)} | (xi , eta , zeta) = (x + lambda , y + lambda ,(x + y*I)+ lambda) |
(\[Xi], \[Eta], \[Zeta]) == (x + \[Lambda], y + \[Lambda],(x + y*I)+ \[Lambda]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mu = \lambda^{-2}\left(\sqrt{xyz}+\sqrt{(x+\lambda)(y+\lambda)(z+\lambda)}\right)^{2}-\lambda-x-y-z} | mu = (lambda)^(- 2)*(sqrt(x*y*(x + y*I))+sqrt((x + lambda)*(y + lambda)*((x + y*I)+ lambda)))^(2)- lambda - x - y -(x + y*I) |
\[Mu] == \[Lambda]^(- 2)*(Sqrt[x*y*(x + y*I)]+Sqrt[(x + \[Lambda])*(y + \[Lambda])*((x + y*I)+ \[Lambda])])^(2)- \[Lambda]- x - y -(x + y*I) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (\lambda\mu-xy-xz-yz)^{2} = 4xyz(\lambda+\mu+x+y+z)} | (lambda*mu - x*y - x*(x + y*I)- y*(x + y*I))^(2) = 4*x*y*(x + y*I)*(lambda + mu + x + y +(x + y*I)) |
(\[Lambda]*\[Mu]- x*y - x*(x + y*I)- y*(x + y*I))^(2) == 4*x*y*(x + y*I)*(\[Lambda]+ \[Mu]+ x + y +(x + y*I)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRD@{x+\lambda}{y+\lambda}{z+\lambda}+\CarlsonsymellintRD@{x+\mu}{y+\mu}{z+\mu} = \CarlsonsymellintRD@{x}{y}{z}-\frac{3}{\sqrt{z(z+\lambda)(z+\mu)}}} | Error |
3*(EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]-EllipticE[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])])/(((x + y*I)+ \[Lambda]-y + \[Lambda])*((x + y*I)+ \[Lambda]-x + \[Lambda])^(1/2))+ 3*(EllipticF[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu])]-EllipticE[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu])])/(((x + y*I)+ \[Mu]-y + \[Mu])*((x + y*I)+ \[Mu]-x + \[Mu])^(1/2)) == 3*(EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/((x + y*I-y)*(x + y*I-x)^(1/2))-Divide[3,Sqrt[(x + y*I)*((x + y*I)+ \[Lambda])*((x + y*I)+ \[Mu])]] |
Missing Macro Error | Aborted | - | Failed [300 / 300]
{Complex[-0.4984590390126629, 1.2092907867192135] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.01924185171185039, 1.9974068077017313] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.26.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRG@{x+\lambda}{y+\lambda}{z+\lambda}+2\CarlsonsymellintRG@{x+\mu}{y+\mu}{z+\mu} = 2\CarlsonsymellintRG@{x}{y}{z}+\lambda\CarlsonsymellintRF@{x+\lambda}{y+\lambda}{z+\lambda}+\mu\CarlsonsymellintRF@{x+\mu}{y+\mu}{z+\mu}+\sqrt{\lambda+\mu+x+y+z}} | Error |
2*Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]]*(EllipticE[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]+(Cot[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]]])^2*EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]+Cot[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]]]^2])+ 2*Sqrt[(x + y*I)+ \[Mu]-x + \[Mu]]*(EllipticE[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu])]+(Cot[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]]])^2*EllipticF[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu])]+Cot[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]]]^2]) == 2*Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2])+ \[Lambda]*EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]/Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]]+ \[Mu]*EllipticF[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu])]/Sqrt[(x + y*I)+ \[Mu]-x + \[Mu]]+Sqrt[\[Lambda]+ \[Mu]+ x + y +(x + y*I)] |
Missing Macro Error | Aborted | - | Failed [300 / 300] {Plus[Complex[-2.0898920996046204, 0.6803615706262403], Times[Complex[-1.7320508075688772, 1.732050807568877], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]], Times[Complex[4.184639587172815, -1.9117536488739475], Plus[Complex[0.7424137617640161, 0.220635885032481], Times[Complex[0.14483575015411373, 1.3558262394954135], Power[Plus[1.0, Times[Complex[0.9940169358562925, 0.4776709006307397], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Plus[Complex[-1.182728387586514, 0.2705509888970101], Times[Complex[-1.7320508075688772, 1.732050807568877], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038]
|
| 19.26.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{x+\lambda}{y+\lambda}{z+\lambda}{p+\lambda}+\CarlsonsymellintRJ@{x+\mu}{y+\mu}{z+\mu}{p+\mu} = \CarlsonsymellintRJ@{x}{y}{z}{p}-3\CarlsonellintRC@{\gamma-\delta}{\gamma}} | Error |
3*((x + y*I)+ \[Lambda]-x + \[Lambda])/((x + y*I)+ \[Lambda]-p + \[Lambda])*(EllipticPi[((x + y*I)+ \[Lambda]-p + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda]),ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]-EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])])/Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]]+ 3*((x + y*I)+ \[Mu]-x + \[Mu])/((x + y*I)+ \[Mu]-p + \[Mu])*(EllipticPi[((x + y*I)+ \[Mu]-p + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu]),ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu])]-EllipticF[ArcCos[Sqrt[x + \[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-x + \[Mu])])/Sqrt[(x + y*I)+ \[Mu]-x + \[Mu]] == 3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x]- 3*1/Sqrt[\[Gamma]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Gamma]- \[Delta])/(\[Gamma])] |
Missing Macro Error | Failure | - | Failed [300 / 300] {Complex[6.482970499990588, -0.8807575715831795] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[γ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[7.020988185402777, -1.8389880807014276] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[γ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[δ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]}</code
|
| 19.26#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma = p(p+\lambda)(p+\mu)} | gamma = p*(p + lambda)*(p + mu) |
\[Gamma] == p*(p + \[Lambda])*(p + \[Mu]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \delta = (p-x)(p-y)(p-z)} | delta = (p - x)*(p - y)*(p -(x + y*I)) |
\[Delta] == (p - x)*(p - y)*(p -(x + y*I)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x+\lambda}{y+\lambda}+\CarlsonellintRC@{x+\mu}{y+\mu} = \CarlsonellintRC@{x}{y}} | Error |
1/Sqrt[y + \[Lambda]]*Hypergeometric2F1[1/2,1/2,3/2,1-(x + \[Lambda])/(y + \[Lambda])]+ 1/Sqrt[y + \[Mu]]*Hypergeometric2F1[1/2,1/2,3/2,1-(x + \[Mu])/(y + \[Mu])] == 1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Complex[1.7722794006718585, -0.740880873447254] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.579678795390187, -0.7154745309495683] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[μ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.26#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x+\mu = \lambda^{-2}(\sqrt{x+\lambda}y+\sqrt{x}(y+\lambda))^{2}} | x + mu = (lambda)^(- 2)*(sqrt(x + lambda)*y +sqrt(x)*(y + lambda))^(2) |
x + \[Mu] == \[Lambda]^(- 2)*(Sqrt[x + \[Lambda]]*y +Sqrt[x]*(y + \[Lambda]))^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y+\mu = (y(y+\lambda)/\lambda^{2})(\sqrt{x}+\sqrt{x+\lambda})^{2}} | y + mu = (y*(y + lambda)/ (lambda)^(2))*(sqrt(x)+sqrt(x + lambda))^(2) |
y + \[Mu] == (y*(y + \[Lambda])/ \[Lambda]^(2))*(Sqrt[x]+Sqrt[x + \[Lambda]])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{\alpha^{2}}{\alpha^{2}-\theta}+\CarlsonellintRC@{\beta^{2}}{\beta^{2}-\theta} = \CarlsonellintRC@{\sigma^{2}}{\sigma^{2}-\theta}} | Error |
1/Sqrt[\[Alpha]^(2)- \[Theta]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Alpha]^(2))/(\[Alpha]^(2)- \[Theta])]+ 1/Sqrt[\[Beta]^(2)- \[Theta]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Beta]^(2))/(\[Beta]^(2)- \[Theta])] == 1/Sqrt[\[Sigma]^(2)- \[Theta]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Sigma]^(2))/(\[Sigma]^(2)- \[Theta])] |
Missing Macro Error | Aborted | - | Successful [Tested: 2] |
| 19.26.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p-y)\CarlsonellintRC@{x}{p}+(q-y)\CarlsonellintRC@{x}{q} = (\eta-\xi)\CarlsonellintRC@{\xi}{\eta}} | Error |
(p - y)* 1/Sqrt[p]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(p)]+(q - y)* 1/Sqrt[q]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(q)] == (\[Eta]- \[Xi])* 1/Sqrt[\[Eta]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Xi])/(\[Eta])] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Indeterminate <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5], Rule[η, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ξ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-3.0971074607887266, 1.6817857583573725] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5], Rule[η, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ξ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.26#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (p-x)(q-x) = (y-x)^{2}} | (p - x)*(q - x) = (y - x)^(2) |
(p - x)*(q - x) == (y - x)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \xi = y^{2}/x} | xi = (y)^(2)/ x |
\[Xi] == (y)^(2)/ x |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta = pq/x} | eta = p*q/ x |
\[Eta] == p*q/ x |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta-\xi = p+q-2y} | eta - xi = p + q - 2*y |
\[Eta]- \[Xi] == p + q - 2*y |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{\lambda}{y+\lambda}{z+\lambda} = {\CarlsonsymellintRF@{0}{y}{z}-\CarlsonsymellintRF@{\mu}{y+\mu}{z+\mu},}} | 0.5*int(1/(sqrt(t+lambda)*sqrt(t+y + lambda)*sqrt(t+(x + y*I)+ lambda)), t = 0..infinity) = 0.5*int(1/(sqrt(t+0)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity)- 0.5*int(1/(sqrt(t+mu)*sqrt(t+y + mu)*sqrt(t+(x + y*I)+ mu)), t = 0..infinity), |
EllipticF[ArcCos[Sqrt[\[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-\[Lambda])]/Sqrt[(x + y*I)+ \[Lambda]-\[Lambda]] == EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0]- EllipticF[ArcCos[Sqrt[\[Mu]/(x + y*I)+ \[Mu]]],((x + y*I)+ \[Mu]-y + \[Mu])/((x + y*I)+ \[Mu]-\[Mu])]/Sqrt[(x + y*I)+ \[Mu]-\[Mu]], |
Error | Failure | - | Error |
| 19.26.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{\alpha}\CarlsonellintRC@{\beta}{\alpha+\beta}+\sqrt{\beta}\CarlsonellintRC@{\alpha}{\alpha+\beta} = \pi/2} | Error |
Sqrt[\[Alpha]]*1/Sqrt[\[Alpha]+ \[Beta]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Beta])/(\[Alpha]+ \[Beta])]+Sqrt[\[Beta]]*1/Sqrt[\[Alpha]+ \[Beta]]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Alpha])/(\[Alpha]+ \[Beta])] == Pi/ 2 |
Missing Macro Error | Failure | - | Successful [Tested: 9] |
| 19.26.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x}{y}{z} = 2\CarlsonsymellintRF@{x+\lambda}{y+\lambda}{z+\lambda}} | 0.5*int(1/(sqrt(t+x)*sqrt(t+y)*sqrt(t+x + y*I)), t = 0..infinity) = 2*0.5*int(1/(sqrt(t+x + lambda)*sqrt(t+y + lambda)*sqrt(t+(x + y*I)+ lambda)), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] == 2*EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]/Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]] |
Aborted | Failure | Skipped - Because timed out | Failed [180 / 180]
{Complex[-0.6992255245511445, 1.8246422705609677] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.7332476531334464, -0.3074481161267689] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.26.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRF@{x+\lambda}{y+\lambda}{z+\lambda} = \CarlsonsymellintRF@{\frac{x+\lambda}{4}}{\frac{y+\lambda}{4}}{\frac{z+\lambda}{4}}} | 2*0.5*int(1/(sqrt(t+x + lambda)*sqrt(t+y + lambda)*sqrt(t+(x + y*I)+ lambda)), t = 0..infinity) = 0.5*int(1/(sqrt(t+(x + lambda)/(4))*sqrt(t+(y + lambda)/(4))*sqrt(t+((x + y*I)+ lambda)/(4))), t = 0..infinity) |
2*EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]/Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]] == EllipticF[ArcCos[Sqrt[Divide[x + \[Lambda],4]/Divide[(x + y*I)+ \[Lambda],4]]],(Divide[(x + y*I)+ \[Lambda],4]-Divide[y + \[Lambda],4])/(Divide[(x + y*I)+ \[Lambda],4]-Divide[x + \[Lambda],4])]/Sqrt[Divide[(x + y*I)+ \[Lambda],4]-Divide[x + \[Lambda],4]] |
Failure | Failure | Skipped - Because timed out | Failed [180 / 180]
{Complex[-1.1343270456997319, -2.101834604175173] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.07907692856233961, -0.3004487668798371] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.26.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lambda = \sqrt{x}\sqrt{y}+\sqrt{y}\sqrt{z}+\sqrt{z}\sqrt{x}} | lambda = sqrt(x)*sqrt(y)+sqrt(y)*sqrt(x + y*I)+sqrt(x + y*I)*sqrt(x) |
\[Lambda] == Sqrt[x]*Sqrt[y]+Sqrt[y]*Sqrt[x + y*I]+Sqrt[x + y*I]*Sqrt[x] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRD@{x}{y}{z} = 2\CarlsonsymellintRD@{x+\lambda}{y+\lambda}{z+\lambda}+\frac{3}{\sqrt{z}(z+\lambda)}} | Error |
3*(EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/((x + y*I-y)*(x + y*I-x)^(1/2)) == 2*3*(EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]-EllipticE[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])])/(((x + y*I)+ \[Lambda]-y + \[Lambda])*((x + y*I)+ \[Lambda]-x + \[Lambda])^(1/2))+Divide[3,Sqrt[x + y*I]*((x + y*I)+ \[Lambda])] |
Missing Macro Error | Failure | - | Failed [180 / 180]
{Complex[0.4984590390126629, -1.2092907867192135] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.5295690158190058, -2.8195127867822802] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.26.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRG@{x}{y}{z} = 4\CarlsonsymellintRG@{x+\lambda}{y+\lambda}{z+\lambda}-\lambda\CarlsonsymellintRF@{x}{y}{z}-\sqrt{x}-\sqrt{y}-\sqrt{z}} | Error |
2*Sqrt[x + y*I-x]*(EllipticE[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+(Cot[ArcCos[Sqrt[x/x + y*I]]])^2*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]+Cot[ArcCos[Sqrt[x/x + y*I]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x/x + y*I]]]^2]) == 4*Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]]*(EllipticE[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]+(Cot[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]]])^2*EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]+Cot[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]]]^2])- \[Lambda]*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x]-Sqrt[x]-Sqrt[y]-Sqrt[x + y*I] |
Missing Macro Error | Aborted | - | Failed [180 / 180] {Plus[Complex[2.330530943809637, 0.9206144902290859], Times[Complex[1.7320508075688772, -1.732050807568877], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]], Times[Complex[-4.184639587172815, 1.9117536488739475], Plus[Complex[0.7424137617640161, 0.220635885032481], Times[Complex[0.14483575015411373, 1.3558262394954135], Power[Plus[1.0, Times[Complex[0.9940169358562925, 0.4776709006307397], Power[k, 2]]], Rational[1, 2]]]]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Plus[Complex[2.3171140130573056, 0.42755423781462054], Times[Complex[1.7320508075688772, -1.732050807568877], Plus[Complex[0.9985512968581824, 0.2012315241723115], Times[Complex[0.3176872874027722, -1.049249833251038], Power[Plus[1.0, Times[Complex[0.0, -1.5], Power[k, 2]]], Rational[1, 2]]]]], Tim
|
| 19.26.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRJ@{x}{y}{z}{p} = 2\CarlsonsymellintRJ@{x+\lambda}{y+\lambda}{z+\lambda}{p+\lambda}+3\CarlsonellintRC@{\alpha^{2}}{\beta^{2}}} | Error |
3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] == 2*3*((x + y*I)+ \[Lambda]-x + \[Lambda])/((x + y*I)+ \[Lambda]-p + \[Lambda])*(EllipticPi[((x + y*I)+ \[Lambda]-p + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda]),ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])]-EllipticF[ArcCos[Sqrt[x + \[Lambda]/(x + y*I)+ \[Lambda]]],((x + y*I)+ \[Lambda]-y + \[Lambda])/((x + y*I)+ \[Lambda]-x + \[Lambda])])/Sqrt[(x + y*I)+ \[Lambda]-x + \[Lambda]]+ 3*1/Sqrt[\[Beta]^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(\[Alpha]^(2))/(\[Beta]^(2))] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Indeterminate <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Indeterminate <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[α, 1.5], Rule[β, 1.5], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.26#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha = p(\sqrt{x}+\sqrt{y}+\sqrt{z})+\sqrt{x}\sqrt{y}\sqrt{z}} | alpha = p*(sqrt(x)+sqrt(y)+sqrt(x + y*I))+sqrt(x)*sqrt(y)*sqrt(x + y*I) |
\[Alpha] == p*(Sqrt[x]+Sqrt[y]+Sqrt[x + y*I])+Sqrt[x]*Sqrt[y]*Sqrt[x + y*I] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta = \sqrt{p}(p+\lambda)} | beta = sqrt(p)*(p + lambda) |
\[Beta] == Sqrt[p]*(p + \[Lambda]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta+\alpha = (\sqrt{p}+\sqrt{x})(\sqrt{p}+\sqrt{y})(\sqrt{p}+\sqrt{z})} | beta + alpha = (sqrt(p)+sqrt(x))*(sqrt(p)+sqrt(y))*(sqrt(p)+sqrt(x + y*I)) |
\[Beta]+ \[Alpha] == (Sqrt[p]+Sqrt[x])*(Sqrt[p]+Sqrt[y])*(Sqrt[p]+Sqrt[x + y*I]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26#Ex14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta^{2}-\alpha^{2} = (p-x)(p-y)(p-z)} | (beta)^(2)- (alpha)^(2) = (p - x)*(p - y)*(p -(x + y*I)) |
\[Beta]^(2)- \[Alpha]^(2) == (p - x)*(p - y)*(p -(x + y*I)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = (\xi\zeta+\eta\zeta-\xi\eta)^{2}/(4\xi\eta\zeta)} | z = (xi*zeta + eta*zeta - xi*eta)^(2)/(4*xi*eta*zeta) |
z == (\[Xi]*\[Zeta]+ \[Eta]*\[Zeta]- \[Xi]*\[Eta])^(2)/(4*\[Xi]*\[Eta]*\[Zeta]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.26.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x}{y} = 2\CarlsonellintRC@{x+\lambda}{y+\lambda}} | Error |
1/Sqrt[y]*Hypergeometric2F1[1/2,1/2,3/2,1-(x)/(y)] == 2*1/Sqrt[y + \[Lambda]]*Hypergeometric2F1[1/2,1/2,3/2,1-(x + \[Lambda])/(y + \[Lambda])] |
Missing Macro Error | Failure | - | Failed [1 / 1]
{Indeterminate <- {Rule[x, 0.5], Rule[y, 0.5], Rule[λ, 1.5]} |
| 19.26.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x^{2}}{y^{2}} = \CarlsonellintRC@{a^{2}}{ay}} | Error |
1/Sqrt[(y)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((y)^(2))] == 1/Sqrt[a*y]*Hypergeometric2F1[1/2,1/2,3/2,1-((a)^(2))/(a*y)] |
Missing Macro Error | Aborted | - | Failed [3 / 3]
{Indeterminate <- {Rule[a, 1.5], Rule[x, 1.5], Rule[y, 1.5]}Indeterminate <- {Rule[a, 0.5], Rule[x, 0.5], Rule[y, 0.5]} |
| 19.26.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{x^{2}}{x^{2}-\theta} = 2\CarlsonellintRC@{s^{2}}{s^{2}-\theta}} | Error |
1/Sqrt[(x)^(2)- \[Theta]]*Hypergeometric2F1[1/2,1/2,3/2,1-((x)^(2))/((x)^(2)- \[Theta])] == 2*1/Sqrt[(s)^(2)- \[Theta]]*Hypergeometric2F1[1/2,1/2,3/2,1-((s)^(2))/((s)^(2)- \[Theta])] |
Missing Macro Error | Failure | - | Successful [Tested: 2] |
| 19.27#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a = \tfrac{1}{2}(x+y)} | a = (1)/(2)*(x + y) |
a == Divide[1,2]*(x + y) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.27#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b = \tfrac{1}{2}(y+z)} | b = (1)/(2)*(y +(x + y*I)) |
b == Divide[1,2]*(y +(x + y*I)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.27#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c = \tfrac{1}{3}(x+y+z)} | c = (1)/(3)*(x + y +(x + y*I)) |
c == Divide[1,3]*(x + y +(x + y*I)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.27#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle f = (xyz)^{1/3}} | f = (x*y*(x + y*I))^(1/ 3) |
f == (x*y*(x + y*I))^(1/ 3) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.27#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle g = (xy)^{1/2}} | g = (x*y)^(1/ 2) |
g == (x*y)^(1/ 2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.27#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle h = (yz)^{1/2}} | h = (y*(x + y*I))^(1/ 2) |
h == (y*(x + y*I))^(1/ 2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.28.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}t^{\sigma-1}\CarlsonsymellintRF@{0}{t}{1}\diff{t} = \tfrac{1}{2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}} | int((t)^(sigma - 1)* 0.5*int(1/(sqrt(t+0)*sqrt(t+t)*sqrt(t+1)), t = 0..infinity), t = 0..1) = (1)/(2)*(Beta(sigma, (1)/(2)))^(2) |
Integrate[(t)^(\[Sigma]- 1)* EllipticF[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]/Sqrt[1-0], {t, 0, 1}, GenerateConditions->None] == Divide[1,2]*(Beta[\[Sigma], Divide[1,2]])^(2) |
Failure | Aborted | Failed [10 / 10] 10/10]: [[Float(undefined)+1.162857938*I <- {sigma = 1/2*3^(1/2)+1/2*I}Float(undefined)+.9984297790*I <- {sigma = -1/2+1/2*I*3^(1/2)} |
Skipped - Because timed out |
| 19.28.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}t^{\sigma-1}\CarlsonsymellintRG@{0}{t}{1}\diff{t} = \frac{\sigma}{4\sigma+2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}} | Error |
Integrate[(t)^(\[Sigma]- 1)* Sqrt[1-0]*(EllipticE[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2*EllipticF[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2]), {t, 0, 1}, GenerateConditions->None] == Divide[\[Sigma],4*\[Sigma]+ 2]*(Beta[\[Sigma], Divide[1,2]])^(2) |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.28.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}t^{\sigma-1}(1-t)\CarlsonsymellintRD@{0}{t}{1}\diff{t} = \frac{3}{4\sigma+2}\left(\EulerBeta@{\sigma}{\tfrac{1}{2}}\right)^{2}} | Error |
Integrate[(t)^(\[Sigma]- 1)*(1 - t)* 3*(EllipticF[ArcCos[Sqrt[0/1]],(1-t)/(1-0)]-EllipticE[ArcCos[Sqrt[0/1]],(1-t)/(1-0)])/((1-t)*(1-0)^(1/2)), {t, 0, 1}, GenerateConditions->None] == Divide[3,4*\[Sigma]+ 2]*(Beta[\[Sigma], Divide[1,2]])^(2) |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.28.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{z}^{\infty}\CarlsonsymellintRD@{x}{y}{t}\diff{t} = 6\CarlsonsymellintRF@{x}{y}{z}} | Error |
Integrate[3*(EllipticF[ArcCos[Sqrt[x/t]],(t-y)/(t-x)]-EllipticE[ArcCos[Sqrt[x/t]],(t-y)/(t-x)])/((t-y)*(t-x)^(1/2)), {t, (x + y*I), Infinity}, GenerateConditions->None] == 6*EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]/Sqrt[x + y*I-x] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.28.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{1}\CarlsonsymellintRD@{x}{y}{v^{2}z+(1-v^{2})p}\diff{v} = \CarlsonsymellintRJ@{x}{y}{z}{p}} | Error |
Integrate[3*(EllipticF[ArcCos[Sqrt[x/(v)^(2)*(x + y*I)+(1 - (v)^(2))* p]],((v)^(2)*(x + y*I)+(1 - (v)^(2))* p-y)/((v)^(2)*(x + y*I)+(1 - (v)^(2))* p-x)]-EllipticE[ArcCos[Sqrt[x/(v)^(2)*(x + y*I)+(1 - (v)^(2))* p]],((v)^(2)*(x + y*I)+(1 - (v)^(2))* p-y)/((v)^(2)*(x + y*I)+(1 - (v)^(2))* p-x)])/(((v)^(2)*(x + y*I)+(1 - (v)^(2))* p-y)*((v)^(2)*(x + y*I)+(1 - (v)^(2))* p-x)^(1/2)), {v, 0, 1}, GenerateConditions->None] == 3*(x + y*I-x)/(x + y*I-p)*(EllipticPi[(x + y*I-p)/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.28.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\CarlsonsymellintRJ@{x}{y}{z}{r^{2}}\diff{r} = \tfrac{3}{2}\pi\CarlsonsymellintRF@{xy}{xz}{yz}} | Error |
Integrate[3*(x + y*I-x)/(x + y*I-(r)^(2))*(EllipticPi[(x + y*I-(r)^(2))/(x + y*I-x),ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)]-EllipticF[ArcCos[Sqrt[x/x + y*I]],(x + y*I-y)/(x + y*I-x)])/Sqrt[x + y*I-x], {r, 0, Infinity}, GenerateConditions->None] == Divide[3,2]*Pi*EllipticF[ArcCos[Sqrt[x*y/y*(x + y*I)]],(y*(x + y*I)-x*(x + y*I))/(y*(x + y*I)-x*y)]/Sqrt[y*(x + y*I)-x*y] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.28.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\CarlsonsymellintRJ@{tx}{y}{z}{tp}\diff{t} = \frac{6}{\sqrt{p}}\CarlsonellintRC@{p}{x}\CarlsonsymellintRF@{0}{y}{z}} | Error |
Integrate[3*(x + y*I-t*x)/(x + y*I-t*p)*(EllipticPi[(x + y*I-t*p)/(x + y*I-t*x),ArcCos[Sqrt[t*x/x + y*I]],(x + y*I-y)/(x + y*I-t*x)]-EllipticF[ArcCos[Sqrt[t*x/x + y*I]],(x + y*I-y)/(x + y*I-t*x)])/Sqrt[x + y*I-t*x], {t, 0, Infinity}, GenerateConditions->None] == Divide[6,Sqrt[p]]*1/Sqrt[x]*Hypergeometric2F1[1/2,1/2,3/2,1-(p)/(x)]*EllipticF[ArcCos[Sqrt[0/x + y*I]],(x + y*I-y)/(x + y*I-0)]/Sqrt[x + y*I-0] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.28.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\pi/2}\CarlsonsymellintRF@{\sin^{2}@@{\theta}\cos^{2}@{x+y}}{\sin^{2}@@{\theta}\cos^{2}@{x-y}}{1}\diff{\theta} = \CarlsonsymellintRF@{0}{\cos^{2}@@{x}}{1}\CarlsonsymellintRF@{0}{\cos^{2}@@{y}}{1}} | int(0.5*int(1/(sqrt(t+(sin(theta))^(2)* (cos(x + y))^(2))*sqrt(t+(sin(theta))^(2)* (cos(x - y))^(2))*sqrt(t+1)), t = 0..infinity), theta = 0..Pi/ 2) = 0.5*int(1/(sqrt(t+0)*sqrt(t+(cos(x))^(2))*sqrt(t+1)), t = 0..infinity)*0.5*int(1/(sqrt(t+0)*sqrt(t+(cos(y))^(2))*sqrt(t+1)), t = 0..infinity) |
Integrate[EllipticF[ArcCos[Sqrt[(Sin[\[Theta]])^(2)* (Cos[x + y])^(2)/1]],(1-(Sin[\[Theta]])^(2)* (Cos[x - y])^(2))/(1-(Sin[\[Theta]])^(2)* (Cos[x + y])^(2))]/Sqrt[1-(Sin[\[Theta]])^(2)* (Cos[x + y])^(2)], {\[Theta], 0, Pi/ 2}, GenerateConditions->None] == EllipticF[ArcCos[Sqrt[0/1]],(1-(Cos[x])^(2))/(1-0)]/Sqrt[1-0]*EllipticF[ArcCos[Sqrt[0/1]],(1-(Cos[y])^(2))/(1-0)]/Sqrt[1-0] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.28.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\CarlsonsymellintRF@{(ac+bd)^{2}}{(ad+bc)^{2}}{4abcd\cosh^{2}@@{z}}\diff{z} = \tfrac{1}{2}\CarlsonsymellintRF@{0}{a^{2}}{b^{2}}\CarlsonsymellintRF@{0}{c^{2}}{d^{2}}} | int(0.5*int(1/(sqrt(t+(a*c + b*d)^(2))*sqrt(t+(a*d + b*c)^(2))*sqrt(t+4*a*b*c*d*(cosh(z))^(2))), t = 0..infinity), z = 0..infinity) = (1)/(2)*0.5*int(1/(sqrt(t+0)*sqrt(t+(a)^(2))*sqrt(t+(b)^(2))), t = 0..infinity)*0.5*int(1/(sqrt(t+0)*sqrt(t+(c)^(2))*sqrt(t+(d)^(2))), t = 0..infinity) |
Integrate[EllipticF[ArcCos[Sqrt[(a*c + b*d)^(2)/4*a*b*c*d*(Cosh[z])^(2)]],(4*a*b*c*d*(Cosh[z])^(2)-(a*d + b*c)^(2))/(4*a*b*c*d*(Cosh[z])^(2)-(a*c + b*d)^(2))]/Sqrt[4*a*b*c*d*(Cosh[z])^(2)-(a*c + b*d)^(2)], {z, 0, Infinity}, GenerateConditions->None] == Divide[1,2]*EllipticF[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]/Sqrt[(b)^(2)-0]*EllipticF[ArcCos[Sqrt[0/(d)^(2)]],((d)^(2)-(c)^(2))/((d)^(2)-0)]/Sqrt[(d)^(2)-0] |
Error | Aborted | - | Skipped - Because timed out |
| 19.29#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle X_{\alpha} = \sqrt{a_{\alpha}+b_{\alpha}x}} | X[alpha] = sqrt(a[alpha]+ b[alpha]*x) |
Subscript[X, \[Alpha]] == Sqrt[Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*x] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Y_{\alpha} = \sqrt{a_{\alpha}+b_{\alpha}y}} | Y[alpha] = sqrt(a[alpha]+ b[alpha]*y) |
Subscript[Y, \[Alpha]] == Sqrt[Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*y] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d_{\alpha\beta} = a_{\alpha}b_{\beta}-a_{\beta}b_{\alpha}} | d[alpha*beta] = a[alpha]*b[beta]- a[beta]*b[alpha] |
Subscript[d, \[Alpha]*\[Beta]] == Subscript[a, \[Alpha]]*Subscript[b, \[Beta]]- Subscript[a, \[Beta]]*Subscript[b, \[Alpha]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s(t) = \prod_{\alpha=1}^{4}\sqrt{a_{\alpha}+b_{\alpha}t}} | s*(t) = product(sqrt(a[alpha]+ b[alpha]*t), alpha = 1..4) |
s*(t) == Product[Sqrt[Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*t], {\[Alpha], 1, 4}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{s(t)} = 2\CarlsonsymellintRF@{U_{12}^{2}}{U_{13}^{2}}{U_{23}^{2}}} | 0.5*int(1/(sqrt(t+U(U[12])^(2))*sqrt(t+U(U[13])^(2))*sqrt(t+U(U[23])^(2))), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[U(Subscript[U, 12])^(2)/U(Subscript[U, 23])^(2)]],(U(Subscript[U, 23])^(2)-U(Subscript[U, 13])^(2))/(U(Subscript[U, 23])^(2)-U(Subscript[U, 12])^(2))]/Sqrt[U(Subscript[U, 23])^(2)-U(Subscript[U, 12])^(2)] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.29#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{\alpha\beta} = (X_{\alpha}X_{\beta}Y_{\gamma}Y_{\delta}+Y_{\alpha}Y_{\beta}X_{\gamma}X_{\delta})/(x-y)} | U[alpha*beta] = (X[alpha]*X[beta]*Y[gamma]*Y[delta]+ Y[alpha]*Y[beta]*X[gamma]*X[delta])/(x - y) |
Subscript[U, \[Alpha]*\[Beta]] == (Subscript[X, \[Alpha]]*Subscript[X, \[Beta]]*Subscript[Y, \[Gamma]]*Subscript[Y, \[Delta]]+ Subscript[Y, \[Alpha]]*Subscript[Y, \[Beta]]*Subscript[X, \[Gamma]]*Subscript[X, \[Delta]])/(x - y) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{\alpha\beta} = U_{\beta\alpha}} | U[alpha*beta] = U[beta*alpha] |
Subscript[U, \[Alpha]*\[Beta]] == Subscript[U, \[Beta]*\[Alpha]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{\alpha\beta}^{2}-U_{\alpha\gamma}^{2} = d_{\alpha\delta}d_{\beta\gamma}} | (U[alpha*beta])^(2)- (U[alpha*gamma])^(2) = d[alpha*delta]*d[beta*gamma] |
(Subscript[U, \[Alpha]*\[Beta]])^(2)- (Subscript[U, \[Alpha]*\[Gamma]])^(2) == Subscript[d, \[Alpha]*\[Delta]]*Subscript[d, \[Beta]*\[Gamma]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{\alpha\beta} = \sqrt{b_{\alpha}}\sqrt{b_{\beta}}Y_{\gamma}Y_{\delta}+Y_{\alpha}Y_{\beta}\sqrt{b_{\gamma}}\sqrt{b_{\delta}},} | U[alpha*beta] = sqrt(b[alpha])*sqrt(b[beta])*Y[gamma]*Y[delta]+ Y[alpha]*Y[beta]*sqrt(b[gamma])*sqrt(b[delta]), |
Subscript[U, \[Alpha]*\[Beta]] == Sqrt[Subscript[b, \[Alpha]]]*Sqrt[Subscript[b, \[Beta]]]*Subscript[Y, \[Gamma]]*Subscript[Y, \[Delta]]+ Subscript[Y, \[Alpha]]*Subscript[Y, \[Beta]]*Sqrt[Subscript[b, \[Gamma]]]*Sqrt[Subscript[b, \[Delta]]], |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{\alpha\beta} = X_{\alpha}X_{\beta}\sqrt{-b_{\gamma}}\sqrt{-b_{\delta}}+\sqrt{-b_{\alpha}}\sqrt{-b_{\beta}}X_{\gamma}X_{\delta}} | U[alpha*beta] = X[alpha]*X[beta]*sqrt(- b[gamma])*sqrt(- b[delta])+sqrt(- b[alpha])*sqrt(- b[beta])*X[gamma]*X[delta] |
Subscript[U, \[Alpha]*\[Beta]] == Subscript[X, \[Alpha]]*Subscript[X, \[Beta]]*Sqrt[- Subscript[b, \[Gamma]]]*Sqrt[- Subscript[b, \[Delta]]]+Sqrt[- Subscript[b, \[Alpha]]]*Sqrt[- Subscript[b, \[Beta]]]*Subscript[X, \[Gamma]]*Subscript[X, \[Delta]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{a_{\alpha}+b_{\alpha}t}{a_{\delta}+b_{\delta}t}\frac{\diff{t}}{s(t)} = \tfrac{2}{3}d_{\alpha\beta}d_{\alpha\gamma}\CarlsonsymellintRD@{U_{\alpha\beta}^{2}}{U_{\alpha\gamma}^{2}}{U_{\alpha\delta}^{2}}+\frac{2X_{\alpha}Y_{\alpha}}{X_{\delta}Y_{\delta}U_{\alpha\delta}}} | Error |
Integrate[Divide[Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*t,Subscript[a, \[Delta]]+ Subscript[b, \[Delta]]*t]*Divide[1,s*(t)], {t, y, x}, GenerateConditions->None] == 3*(EllipticF[ArcCos[Sqrt[U(Subscript[U, \[Alpha]*\[Beta]])^(2)/U(Subscript[U, \[Alpha]*\[Delta]])^(2)]],(U(Subscript[U, \[Alpha]*\[Delta]])^(2)-U(Subscript[U, \[Alpha]*\[Gamma]])^(2))/(U(Subscript[U, \[Alpha]*\[Delta]])^(2)-U(Subscript[U, \[Alpha]*\[Beta]])^(2))]-EllipticE[ArcCos[Sqrt[U(Subscript[U, \[Alpha]*\[Beta]])^(2)/U(Subscript[U, \[Alpha]*\[Delta]])^(2)]],(U(Subscript[U, \[Alpha]*\[Delta]])^(2)-U(Subscript[U, \[Alpha]*\[Gamma]])^(2))/(U(Subscript[U, \[Alpha]*\[Delta]])^(2)-U(Subscript[U, \[Alpha]*\[Beta]])^(2))])/((U(Subscript[U, \[Alpha]*\[Delta]])^(2)-U(Subscript[U, \[Alpha]*\[Gamma]])^(2))*(U(Subscript[U, \[Alpha]*\[Delta]])^(2)-U(Subscript[U, \[Alpha]*\[Beta]])^(2))^(1/2))+Divide[2*Subscript[X, \[Alpha]]*Subscript[Y, \[Alpha]],Subscript[X, \[Delta]]*Subscript[Y, \[Delta]]*Subscript[U, \[Alpha]*\[Delta]]] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.29.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{a_{\alpha}+b_{\alpha}t}{a_{5}+b_{5}t}\frac{\diff{t}}{s(t)} = \frac{2}{3}\frac{d_{\alpha\beta}d_{\alpha\gamma}d_{\alpha\delta}}{d_{\alpha 5}}\CarlsonsymellintRJ@{U_{12}^{2}}{U_{13}^{2}}{U_{23}^{2}}{U_{\alpha 5}^{2}}+2\CarlsonellintRC@{S_{\alpha 5}^{2}}{Q_{\alpha 5}^{2}}} | Error |
3*(U(Subscript[U, 23])^(2)-U(Subscript[U, 12])^(2))/(U(Subscript[U, 23])^(2)-U(Subscript[U, \[Alpha]*5])^(2))*(EllipticPi[(U(Subscript[U, 23])^(2)-U(Subscript[U, \[Alpha]*5])^(2))/(U(Subscript[U, 23])^(2)-U(Subscript[U, 12])^(2)),ArcCos[Sqrt[U(Subscript[U, 12])^(2)/U(Subscript[U, 23])^(2)]],(U(Subscript[U, 23])^(2)-U(Subscript[U, 13])^(2))/(U(Subscript[U, 23])^(2)-U(Subscript[U, 12])^(2))]-EllipticF[ArcCos[Sqrt[U(Subscript[U, 12])^(2)/U(Subscript[U, 23])^(2)]],(U(Subscript[U, 23])^(2)-U(Subscript[U, 13])^(2))/(U(Subscript[U, 23])^(2)-U(Subscript[U, 12])^(2))])/Sqrt[U(Subscript[U, 23])^(2)-U(Subscript[U, 12])^(2)]1/Sqrt[Q(Subscript[Q, \[Alpha]*5])^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-(S(Subscript[S, \[Alpha]*5])^(2))/(Q(Subscript[Q, \[Alpha]*5])^(2))] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.29#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle U_{\alpha 5}^{2} = U_{\alpha\beta}^{2}-\frac{d_{\alpha\gamma}d_{\alpha\delta}d_{\beta 5}}{d_{\alpha 5}}} | (U[alpha*5])^(2) = (U[alpha*beta])^(2)-(d[alpha*gamma]*d[alpha*delta]*d[beta*5])/(d[alpha*5]) |
(Subscript[U, \[Alpha]*5])^(2) == (Subscript[U, \[Alpha]*\[Beta]])^(2)-Divide[Subscript[d, \[Alpha]*\[Gamma]]*Subscript[d, \[Alpha]*\[Delta]]*Subscript[d, \[Beta]*5],Subscript[d, \[Alpha]*5]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S_{\alpha 5} = \frac{1}{x-y}\left(\frac{X_{\beta}X_{\gamma}X_{\delta}}{X_{\alpha}}Y_{5}^{2}+\frac{Y_{\beta}Y_{\gamma}Y_{\delta}}{Y_{\alpha}}X_{5}^{2}\right)} | S[alpha*5] ((X[beta]*X[gamma]*X[delta])/(X[alpha])*Y(Y[5])^(2)+(Y[beta]*Y[gamma]*Y[delta])/(Y[alpha])*X(X[5])^(2)) |
Subscript[S, \[Alpha]*5] (Divide[Subscript[X, \[Beta]]*Subscript[X, \[Gamma]]*Subscript[X, \[Delta]],Subscript[X, \[Alpha]]]*Y(Subscript[Y, 5])^(2)+Divide[Subscript[Y, \[Beta]]*Subscript[Y, \[Gamma]]*Subscript[Y, \[Delta]],Subscript[Y, \[Alpha]]]*X(Subscript[X, 5])^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Q_{\alpha 5} = \frac{X_{5}Y_{5}}{X_{\alpha}Y_{\alpha}}U_{\alpha 5}} | Q[alpha*5] = (X[5]*Y[5])/(X[alpha]*Y[alpha])*U[alpha*5] |
Subscript[Q, \[Alpha]*5] == Divide[Subscript[X, 5]*Subscript[Y, 5],Subscript[X, \[Alpha]]*Subscript[Y, \[Alpha]]]*Subscript[U, \[Alpha]*5] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S_{\alpha 5}^{2}-Q_{\alpha 5}^{2} = \frac{d_{\beta 5}d_{\gamma 5}d_{\delta 5}}{d_{\alpha 5}}} | (S[alpha*5])^(2)- (Q[alpha*5])^(2) = (d[beta*5]*d[gamma*5]*d[delta*5])/(d[alpha*5]) |
(Subscript[S, \[Alpha]*5])^(2)- (Subscript[Q, \[Alpha]*5])^(2) == Divide[Subscript[d, \[Beta]*5]*Subscript[d, \[Gamma]*5]*Subscript[d, \[Delta]*5],Subscript[d, \[Alpha]*5]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{u}^{b}\sqrt{\frac{a-t}{(b-t)(t-c)^{3}}}\diff{t} = -\tfrac{2}{3}{(a-b)}{(b-u)}^{3/2}\CarlsonsymellintRD@@{(a-b)(u-c)}{(b-c)(a-u)}{(a-b)(b-c)}+\frac{2}{b-c}\sqrt{\frac{(a-u)(b-u)}{u-c}}} | Error |
Integrate[Sqrt[Divide[a - t,(b - t)*(t - c)^(3)]], {t, u, b}, GenerateConditions->None] == -Divide[2,3]*(a - b)*(b - u)^(3/ 2)* 3*(EllipticF[ArcCos[Sqrt[(a - b)*(u - c)/(a - b)*(b - c)]],((a - b)*(b - c)-(b - c)*(a - u))/((a - b)*(b - c)-(a - b)*(u - c))]-EllipticE[ArcCos[Sqrt[(a - b)*(u - c)/(a - b)*(b - c)]],((a - b)*(b - c)-(b - c)*(a - u))/((a - b)*(b - c)-(a - b)*(u - c))])/(((a - b)*(b - c)-(b - c)*(a - u))*((a - b)*(b - c)-(a - b)*(u - c))^(1/2))+Divide[2,b - c]*Sqrt[Divide[(a - u)*(b - u),u - c]] |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.29.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle I(\mathbf{m}) = \int_{y}^{x}\prod_{\alpha=1}^{h}(a_{\alpha}+b_{\alpha}t)^{-1/2}\prod_{j=1}^{n}(a_{j}+b_{j}t)^{m_{j}}\diff{t}} | I*(m) = int(product((a[alpha]+ b[alpha]*t)^(- 1/ 2)* product((a[j]+ b[j]*t)^(m[j]), j = 1..n), alpha = 1..h), t = y..x) |
I*(m) == Integrate[Product[(Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*t)^(- 1/ 2)* Product[(Subscript[a, j]+ Subscript[b, j]*t)^(Subscript[m, j]), {j, 1, n}, GenerateConditions->None], {\[Alpha], 1, h}, GenerateConditions->None], {t, y, x}, GenerateConditions->None] |
Aborted | Aborted | Error | Skipped - Because timed out |
| 19.29.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{j}I(\mathbf{e}_{l}-\mathbf{e}_{j}) = d_{lj}I(-\mathbf{e}_{j})+b_{l}I(\boldsymbol{{0}})} | b[j]*I*(e[l]- e[j]) = d[l*j]*I*(- e[j])+ b[l]*I*(0) |
Subscript[b, j]*I*(Subscript[e, l]- Subscript[e, j]) == Subscript[d, l*j]*I*(- Subscript[e, j])+ Subscript[b, l]*I*(0) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{\beta}b_{\gamma}I(\mathbf{e}_{\alpha}) = d_{\alpha\beta}d_{\alpha\gamma}I(-\mathbf{e}_{\alpha})+2b_{\alpha}\left(\frac{s(x)}{a_{\alpha}+b_{\alpha}x}-\frac{s(y)}{a_{\alpha}+b_{\alpha}y}\right)} | b[beta]*b[gamma]*I*(e[alpha]) = d[alpha*beta]*d[alpha*gamma]*I*(- e[alpha])+ 2*b[alpha]*((s*(x))/(a[alpha]+ b[alpha]*x)-(s*(y))/(a[alpha]+ b[alpha]*y)) |
Subscript[b, \[Beta]]*Subscript[b, \[Gamma]]*I*(Subscript[e, \[Alpha]]) == Subscript[d, \[Alpha]*\[Beta]]*Subscript[d, \[Alpha]*\[Gamma]]*I*(- Subscript[e, \[Alpha]])+ 2*Subscript[b, \[Alpha]]*(Divide[s*(x),Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*x]-Divide[s*(y),Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*y]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s(t) = \prod_{\alpha=1}^{3}\sqrt{a_{\alpha}+b_{\alpha}t}} | s*(t) = product(sqrt(a[alpha]+ b[alpha]*t), alpha = 1..3) |
s*(t) == Product[Sqrt[Subscript[a, \[Alpha]]+ Subscript[b, \[Alpha]]*t], {\[Alpha], 1, 3}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{j}^{q}I(q\mathbf{e}_{l}) = \sum_{r=0}^{q}\binom{q}{r}b_{l}^{r}d_{lj}^{q-r}I(r\mathbf{e}_{j})} | (b[j])^(q)*I*sum(binomial(q,r)*b(b[l])^(r)*d(d[l*j])^(q - r)*I*(r*e[j]), r = 0..q) |
(Subscript[b, j])^(q)*I*Sum[Binomial[q,r]*b(Subscript[b, l])^(r)*d(Subscript[d, l*j])^(q - r)*I*(r*Subscript[e, j]), {r, 0, q}, GenerateConditions->None] |
Failure | Failure | Error | Skipped - Because timed out |
| 19.29.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{\sqrt{Q_{1}(t)Q_{2}(t)}} = \CarlsonsymellintRF@{U^{2}+a_{1}b_{2}}{U^{2}+a_{2}b_{1}}{U^{2}}} | int((1)/(sqrt(Q[1]*(t)* Q[2]*(t))), t = y..x) = 0.5*int(1/(sqrt(t+(U)^(2)+ a[1]*b[2])*sqrt(t+(U)^(2)+ a[2]*b[1])*sqrt(t+(U)^(2))), t = 0..infinity) |
Integrate[Divide[1,Sqrt[Subscript[Q, 1]*(t)* Subscript[Q, 2]*(t)]], {t, y, x}, GenerateConditions->None] == EllipticF[ArcCos[Sqrt[(U)^(2)+ Subscript[a, 1]*Subscript[b, 2]/(U)^(2)]],((U)^(2)-(U)^(2)+ Subscript[a, 2]*Subscript[b, 1])/((U)^(2)-(U)^(2)+ Subscript[a, 1]*Subscript[b, 2])]/Sqrt[(U)^(2)-(U)^(2)+ Subscript[a, 1]*Subscript[b, 2]] |
Aborted | Aborted | Manual Skip! | Skipped - Because timed out |
| 19.29.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{t^{2}\diff{t}}{\sqrt{Q_{1}(t)Q_{2}(t)}} = \tfrac{1}{3}a_{1}a_{2}\CarlsonsymellintRD@{U^{2}+a_{1}b_{2}}{U^{2}+a_{2}b_{1}}{U^{2}}+(xy/U)} | Error |
Integrate[Divide[(t)^(2),Sqrt[Subscript[Q, 1]*(t)* Subscript[Q, 2]*(t)]], {t, y, x}, GenerateConditions->None] == Divide[1,3]*Subscript[a, 1]*Subscript[a, 2]*3*(EllipticF[ArcCos[Sqrt[(U)^(2)+ Subscript[a, 1]*Subscript[b, 2]/(U)^(2)]],((U)^(2)-(U)^(2)+ Subscript[a, 2]*Subscript[b, 1])/((U)^(2)-(U)^(2)+ Subscript[a, 1]*Subscript[b, 2])]-EllipticE[ArcCos[Sqrt[(U)^(2)+ Subscript[a, 1]*Subscript[b, 2]/(U)^(2)]],((U)^(2)-(U)^(2)+ Subscript[a, 2]*Subscript[b, 1])/((U)^(2)-(U)^(2)+ Subscript[a, 1]*Subscript[b, 2])])/(((U)^(2)-(U)^(2)+ Subscript[a, 2]*Subscript[b, 1])*((U)^(2)-(U)^(2)+ Subscript[a, 1]*Subscript[b, 2])^(1/2))+(x*y/ U) |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.29.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{t^{2}\sqrt{Q_{1}(t)Q_{2}(t)}} = \tfrac{1}{3}b_{1}b_{2}\CarlsonsymellintRD@{U^{2}+a_{1}b_{2}}{U^{2}+a_{2}b_{1}}{U^{2}}+(xyU)^{-1}} | Error |
Integrate[Divide[1,(t)^(2)*Sqrt[Subscript[Q, 1]*(t)* Subscript[Q, 2]*(t)]], {t, y, x}, GenerateConditions->None] == Divide[1,3]*Subscript[b, 1]*Subscript[b, 2]*3*(EllipticF[ArcCos[Sqrt[(U)^(2)+ Subscript[a, 1]*Subscript[b, 2]/(U)^(2)]],((U)^(2)-(U)^(2)+ Subscript[a, 2]*Subscript[b, 1])/((U)^(2)-(U)^(2)+ Subscript[a, 1]*Subscript[b, 2])]-EllipticE[ArcCos[Sqrt[(U)^(2)+ Subscript[a, 1]*Subscript[b, 2]/(U)^(2)]],((U)^(2)-(U)^(2)+ Subscript[a, 2]*Subscript[b, 1])/((U)^(2)-(U)^(2)+ Subscript[a, 1]*Subscript[b, 2])])/(((U)^(2)-(U)^(2)+ Subscript[a, 2]*Subscript[b, 1])*((U)^(2)-(U)^(2)+ Subscript[a, 1]*Subscript[b, 2])^(1/2))+(x*y*U)^(- 1) |
Missing Macro Error | Aborted | - | Skipped - Because timed out |
| 19.29.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (x^{2}-y^{2})U = x\sqrt{Q_{1}(y)Q_{2}(y)}+y\sqrt{Q_{1}(x)Q_{2}(x)}} | ((x)^(2)- (y)^(2))* U = x*sqrt(Q[1]*(y)* Q[2]*(y))+ y*sqrt(Q[1]*(x)* Q[2]*(x)) |
((x)^(2)- (y)^(2))* U == x*Sqrt[Subscript[Q, 1]*(y)* Subscript[Q, 2]*(y)]+ y*Sqrt[Subscript[Q, 1]*(x)* Subscript[Q, 2]*(x)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{\infty}\frac{\diff{t}}{\sqrt{(t^{2}+a^{2})(t^{2}-b^{2})}} = \CarlsonsymellintRF@{y^{2}+a^{2}}{y^{2}-b^{2}}{y^{2}}} | int((1)/(sqrt(((t)^(2)+ (a)^(2))*((t)^(2)- (b)^(2)))), t = y..infinity) = 0.5*int(1/(sqrt(t+(y)^(2)+ (a)^(2))*sqrt(t+(y)^(2)- (b)^(2))*sqrt(t+(y)^(2))), t = 0..infinity) |
Integrate[Divide[1,Sqrt[((t)^(2)+ (a)^(2))*((t)^(2)- (b)^(2))]], {t, y, Infinity}, GenerateConditions->None] == EllipticF[ArcCos[Sqrt[(y)^(2)+ (a)^(2)/(y)^(2)]],((y)^(2)-(y)^(2)- (b)^(2))/((y)^(2)-(y)^(2)+ (a)^(2))]/Sqrt[(y)^(2)-(y)^(2)+ (a)^(2)] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.29.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{\sqrt{Q_{1}(t)Q_{2}(t)}} = 4\CarlsonsymellintRF@{U}{U+D_{12}+V}{U+D_{12}-V}} | int((1)/(sqrt(Q[1]*(t)* Q[2]*(t))), t = y..x) = 4*0.5*int(1/(sqrt(t+U)*sqrt(t+U + D[12]+ V)*sqrt(t+U + D[12]- V)), t = 0..infinity) |
Integrate[Divide[1,Sqrt[Subscript[Q, 1]*(t)* Subscript[Q, 2]*(t)]], {t, y, x}, GenerateConditions->None] == 4*EllipticF[ArcCos[Sqrt[U/U + Subscript[D, 12]- V]],(U + Subscript[D, 12]- V-U + Subscript[D, 12]+ V)/(U + Subscript[D, 12]- V-U)]/Sqrt[U + Subscript[D, 12]- V-U] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.29#Ex17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (x-y)^{2}U = S_{1}S_{2}} | (x - y)^(2)* U = S[1]*S[2] |
(x - y)^(2)* U == Subscript[S, 1]*Subscript[S, 2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S_{j} = \left(\sqrt{Q_{j}(x)}+\sqrt{Q_{j}(y)}\right)^{2}-h_{j}(x-y)^{2}} | S[j] = (sqrt(Q[j]*(x))+sqrt(Q[j]*(y)))^(2)- h[j]*(x - y)^(2) |
Subscript[S, j] == (Sqrt[Subscript[Q, j]*(x)]+Sqrt[Subscript[Q, j]*(y)])^(2)- Subscript[h, j]*(x - y)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{jl} = 2f_{j}h_{l}+2h_{j}f_{l}-g_{j}g_{l}} | D[j*l] = 2*f[j]*h[l]+ 2*h[j]*f[l]- g[j]*g[l] |
Subscript[D, j*l] == 2*Subscript[f, j]*Subscript[h, l]+ 2*Subscript[h, j]*Subscript[f, l]- Subscript[g, j]*Subscript[g, l] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle V = \sqrt{D_{12}^{2}-D_{11}D_{22}}} | V sqrt(D(D[12])^(2)- D[11]*D[22]) |
V Sqrt[D(Subscript[D, 12])^(2)- Subscript[D, 11]*Subscript[D, 22]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S_{1} = (X_{1}Y_{2}+Y_{1}X_{2})^{2}} | S[1] = (X[1]*Y[2]+ Y[1]*X[2])^(2) |
Subscript[S, 1] == (Subscript[X, 1]*Subscript[Y, 2]+ Subscript[Y, 1]*Subscript[X, 2])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle X_{j} = \sqrt{a_{j}+b_{j}x}} | X[j] = sqrt(a[j]+ b[j]*x) |
Subscript[X, j] == Sqrt[Subscript[a, j]+ Subscript[b, j]*x] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Y_{j} = \sqrt{a_{j}+b_{j}y}} | Y[j] = sqrt(a[j]+ b[j]*y) |
Subscript[Y, j] == Sqrt[Subscript[a, j]+ Subscript[b, j]*y] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{12} = 2a_{1}a_{2}h_{2}+2b_{1}b_{2}f_{2}-(a_{1}b_{2}+a_{2}b_{1})g_{2}} | D[12] = 2*a[1]*a[2]*h[2]+ 2*b[1]*b[2]*f[2]-(a[1]*b[2]+ a[2]*b[1])* g[2] |
Subscript[D, 12] == 2*Subscript[a, 1]*Subscript[a, 2]*Subscript[h, 2]+ 2*Subscript[b, 1]*Subscript[b, 2]*Subscript[f, 2]-(Subscript[a, 1]*Subscript[b, 2]+ Subscript[a, 2]*Subscript[b, 1])* Subscript[g, 2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{11} = -(a_{1}b_{2}-a_{2}b_{1})^{2}} | D[11] = -(a[1]*b[2]- a[2]*b[1])^(2) |
Subscript[D, 11] == -(Subscript[a, 1]*Subscript[b, 2]- Subscript[a, 2]*Subscript[b, 1])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S_{1} = (X_{1}+Y_{1})^{2}} | S[1] = (X[1]+ Y[1])^(2) |
Subscript[S, 1] == (Subscript[X, 1]+ Subscript[Y, 1])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{12} = 2a_{1}h_{2}-b_{1}g_{2}} | D[12] = 2*a[1]*h[2]- b[1]*g[2] |
Subscript[D, 12] == 2*Subscript[a, 1]*Subscript[h, 2]- Subscript[b, 1]*Subscript[g, 2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle D_{11} = -b_{1}^{2}} | D[11] = - (b[1])^(2) |
Subscript[D, 11] == - (Subscript[b, 1])^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{\sqrt{t^{3}-a^{3}}} = 4\CarlsonsymellintRF@{U}{U-3a+2\sqrt{3}a}{U-3a-2\sqrt{3}a}} | int((1)/(sqrt((t)^(3)- (a)^(3))), t = y..x) = 4*0.5*int(1/(sqrt(t+U)*sqrt(t+U - 3*a + 2*sqrt(3)*a)*sqrt(t+U - 3*a - 2*sqrt(3)*a)), t = 0..infinity) |
Integrate[Divide[1,Sqrt[(t)^(3)- (a)^(3)]], {t, y, x}, GenerateConditions->None] == 4*EllipticF[ArcCos[Sqrt[U/U - 3*a - 2*Sqrt[3]*a]],(U - 3*a - 2*Sqrt[3]*a-U - 3*a + 2*Sqrt[3]*a)/(U - 3*a - 2*Sqrt[3]*a-U)]/Sqrt[U - 3*a - 2*Sqrt[3]*a-U] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.29#Ex29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (x-y)^{2}U = (\sqrt{x-a}+\sqrt{y-a})^{2}\left((\xi+\eta)^{2}-(x-y)^{2}\right)} | (x - y)^(2)* U = (sqrt(x - a)+sqrt(y - a))^(2)*((xi + eta)^(2)-(x - y)^(2)) |
(x - y)^(2)* U == (Sqrt[x - a]+Sqrt[y - a])^(2)*((\[Xi]+ \[Eta])^(2)-(x - y)^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \xi = \sqrt{x^{2}+ax+a^{2}}} | xi = sqrt((x)^(2)+ a*x + (a)^(2)) |
\[Xi] == Sqrt[(x)^(2)+ a*x + (a)^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29#Ex31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta = \sqrt{y^{2}+ay+a^{2}}} | eta = sqrt((y)^(2)+ a*y + (a)^(2)) |
\[Eta] == Sqrt[(y)^(2)+ a*y + (a)^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{\sqrt{Q(t^{2})}} = 2\CarlsonsymellintRF@{U}{U-g+2\sqrt{fh}}{U-g-2\sqrt{fh}}} | int((1)/(sqrt(Q*((t)^(2)))), t = y..x) = 2*0.5*int(1/(sqrt(t+U)*sqrt(t+U - g + 2*sqrt(f*h))*sqrt(t+U - g - 2*sqrt(f*h))), t = 0..infinity) |
Integrate[Divide[1,Sqrt[Q*((t)^(2))]], {t, y, x}, GenerateConditions->None] == 2*EllipticF[ArcCos[Sqrt[U/U - g - 2*Sqrt[f*h]]],(U - g - 2*Sqrt[f*h]-U - g + 2*Sqrt[f*h])/(U - g - 2*Sqrt[f*h]-U)]/Sqrt[U - g - 2*Sqrt[f*h]-U] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.29.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (x-y)^{2}U = \left(\sqrt{Q(x^{2})}+\sqrt{Q(y^{2})}\right)^{2}-h(x^{2}-y^{2})^{2}} | (x - y)^(2)* U = (sqrt(Q*((x)^(2)))+sqrt(Q*((y)^(2))))^(2)- h*((x)^(2)- (y)^(2))^(2) |
(x - y)^(2)* U == (Sqrt[Q*((x)^(2))]+Sqrt[Q*((y)^(2))])^(2)- h*((x)^(2)- (y)^(2))^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.29.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{y}^{x}\frac{\diff{t}}{\sqrt{t^{4}+a^{4}}} = 2\CarlsonsymellintRF@{U}{U+2a^{2}}{U-2a^{2}}} | int((1)/(sqrt((t)^(4)+ (a)^(4))), t = y..x) = 2*0.5*int(1/(sqrt(t+U)*sqrt(t+U + 2*(a)^(2))*sqrt(t+U - 2*(a)^(2))), t = 0..infinity) |
Integrate[Divide[1,Sqrt[(t)^(4)+ (a)^(4)]], {t, y, x}, GenerateConditions->None] == 2*EllipticF[ArcCos[Sqrt[U/U - 2*(a)^(2)]],(U - 2*(a)^(2)-U + 2*(a)^(2))/(U - 2*(a)^(2)-U)]/Sqrt[U - 2*(a)^(2)-U] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Complex[0.06910876495694751, 1.480960979386122] <- {Rule[a, -1.5], Rule[U, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5]}Complex[1.3051585498245286, 1.480960979386122] <- {Rule[a, -1.5], Rule[U, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, 1.5]} |
| 19.29.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (x-y)^{2}U = \left(\sqrt{x^{4}+a^{4}}+\sqrt{y^{4}+a^{4}}\right)^{2}-(x^{2}-y^{2})^{2}} | (x - y)^(2)* U = (sqrt((x)^(4)+ (a)^(4))+sqrt((y)^(4)+ (a)^(4)))^(2)-((x)^(2)- (y)^(2))^(2) |
(x - y)^(2)* U == (Sqrt[(x)^(4)+ (a)^(4)]+Sqrt[(y)^(4)+ (a)^(4)])^(2)-((x)^(2)- (y)^(2))^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.30#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = a\sin@@{\phi}} | x = a*sin(phi) |
x == a*Sin[\[Phi]] |
Failure | Failure | Failed [180 / 180] 180/180]: [[2.788470502+.5063946946*I <- {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, x = 3/2}1.788470502+.5063946946*I <- {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, x = 1/2} |
Failed [180 / 180]
{Complex[2.1491827752870476, 0.34394646701016035] <- {Rule[a, -1.5], Rule[x, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.093555858156998, 0.6491787480429551] <- {Rule[a, -1.5], Rule[x, 1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.30#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = b\cos@@{\phi}} | y = b*cos(phi) |
y == b*Cos[\[Phi]] |
Failure | Failure | Failed [108 / 108] 108/108]: [[-1.393894198 <- {b = -3/2, phi = 3/2, y = -3/2}1.606105802 <- {b = -3/2, phi = 3/2, y = 3/2} |
Failed [108 / 108]
{-1.3938941974984456 <- {Rule[b, -1.5], Rule[y, -1.5], Rule[ϕ, 1.5]}-0.18362615716444086 <- {Rule[b, -1.5], Rule[y, -1.5], Rule[ϕ, 0.5]} |
| 19.30.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s = a\int_{0}^{\phi}\sqrt{1-k^{2}\sin^{2}@@{\theta}}\diff{\theta}} | s = a*int(sqrt(1 - (k)^(2)* (sin(theta))^(2)), theta = 0..phi) |
s == a*Integrate[Sqrt[1 - (k)^(2)* (Sin[\[Theta]])^(2)], {\[Theta], 0, \[Phi]}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.30.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s/a = \incellintEk@{\phi}{k}} | s/ a = EllipticE(sin(phi), k) |
s/ a == EllipticE[\[Phi], (k)^2] |
Failure | Failure | Failed [300 / 300] 300/300]: [[.1410196655-.3375964631*I <- {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, s = -3/2, k = 1}-.36391978e-1+.5433649104e-1*I <- {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, s = -3/2, k = 2} |
Failed [300 / 300]
{Complex[0.5672114831419685, -0.22929764467344024] <- {Rule[a, -1.5], Rule[k, 1], Rule[s, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.5579190406370536, -0.16535187593702125] <- {Rule[a, -1.5], Rule[k, 2], Rule[s, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.30.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \incellintEk@{\phi}{k} = {\CarlsonsymellintRF@{c-1}{c-k^{2}}{c}-\tfrac{1}{3}k^{2}\CarlsonsymellintRD@{c-1}{c-k^{2}}{c}}} | Error |
EllipticE[\[Phi], (k)^2] == EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1]-Divide[1,3]*(k)^(2)* 3*(EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]-EllipticE[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)])/((c-c - (k)^(2))*(c-c - 1)^(1/2)) |
Missing Macro Error | Failure | Skip - symbolical successful subtest | Failed [180 / 180]
{Complex[3.5743811704478246, 0.7698502565730785] <- {Rule[c, -1.5], Rule[k, 1], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[3.9424508382496875, -1.017653751864599] <- {Rule[c, -1.5], Rule[k, 2], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.30#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2} = 1-(b^{2}/a^{2})} | (k)^(2) = 1 -((b)^(2)/ (a)^(2)) |
(k)^(2) == 1 -((b)^(2)/ (a)^(2)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.30#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c = \csc^{2}@@{\phi}} | c = (csc(phi))^(2) |
c == (Csc[\[Phi]])^(2) |
Failure | Failure | Failed [60 / 60] 60/60]: [[-2.359812877+.7993130071*I <- {c = -3/2, phi = 1/2*3^(1/2)+1/2*I}-1.296085040-.8173084059*I <- {c = -3/2, phi = -1/2+1/2*I*3^(1/2)} |
Failed [60 / 60]
{Complex[-3.841312467237177, 3.4490957612740374] <- {Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.17530792640393877, -3.4502399957777015] <- {Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.30.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L(a,b) = 4a\compellintEk@{k}} | L*(a , b) = 4*a*EllipticE(k) |
L*(a , b) == 4*a*EllipticE[(k)^2] |
Failure | Failure | Failed [300 / 300] 300/300]: [[(.8660254040+.5000000000*I)*(-1.500000000, -1.500000000)+6.000000000 <- {L = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, k = 1}(.8660254040+.5000000000*I)*(-1.500000000, -1.500000000)+2.437793319+8.063125386*I <- {L = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, k = 2} |
Error |
| 19.30.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 4a\compellintEk@{k} = 8a\CarlsonsymellintRG@{0}{b^{2}/a^{2}}{1}} | Error |
4*a*EllipticE[(k)^2] == 8*a*Sqrt[1-0]*(EllipticE[ArcCos[Sqrt[0/1]],(1-(b)^(2)/ (a)^(2))/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2*EllipticF[ArcCos[Sqrt[0/1]],(1-(b)^(2)/ (a)^(2))/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2]) |
Missing Macro Error | Failure | Skip - symbolical successful subtest | Failed [108 / 108]
{12.849555921538759 <- {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 1]}Complex[16.411762602778996, -8.063125388322588] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 2]} |
| 19.30.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 8a\CarlsonsymellintRG@{0}{b^{2}/a^{2}}{1} = 8\CarlsonsymellintRG@{0}{a^{2}}{b^{2}}} | Error |
8*a*Sqrt[1-0]*(EllipticE[ArcCos[Sqrt[0/1]],(1-(b)^(2)/ (a)^(2))/(1-0)]+(Cot[ArcCos[Sqrt[0/1]]])^2*EllipticF[ArcCos[Sqrt[0/1]],(1-(b)^(2)/ (a)^(2))/(1-0)]+Cot[ArcCos[Sqrt[0/1]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/1]]]^2]) == 8*Sqrt[(b)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(b)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+Cot[ArcCos[Sqrt[0/(b)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(b)^(2)]]]^2]) |
Missing Macro Error | Failure | Skip - symbolical successful subtest | Failed [18 / 36]
{-37.69911184307752 <- {Rule[a, -1.5], Rule[b, -1.5]}-37.69911184307752 <- {Rule[a, -1.5], Rule[b, 1.5]} |
| 19.30.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 8\CarlsonsymellintRG@{0}{a^{2}}{b^{2}} = 8ab\CarlsonsymellintRG@{0}{a^{-2}}{b^{-2}}} | Error |
8*Sqrt[(b)^(2)-0]*(EllipticE[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+(Cot[ArcCos[Sqrt[0/(b)^(2)]]])^2*EllipticF[ArcCos[Sqrt[0/(b)^(2)]],((b)^(2)-(a)^(2))/((b)^(2)-0)]+Cot[ArcCos[Sqrt[0/(b)^(2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(b)^(2)]]]^2]) == 8*a*b*Sqrt[(b)^(- 2)-0]*(EllipticE[ArcCos[Sqrt[0/(b)^(- 2)]],((b)^(- 2)-(a)^(- 2))/((b)^(- 2)-0)]+(Cot[ArcCos[Sqrt[0/(b)^(- 2)]]])^2*EllipticF[ArcCos[Sqrt[0/(b)^(- 2)]],((b)^(- 2)-(a)^(- 2))/((b)^(- 2)-0)]+Cot[ArcCos[Sqrt[0/(b)^(- 2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[0/(b)^(- 2)]]]^2]) |
Missing Macro Error | Failure | Skip - symbolical successful subtest | Failed [18 / 36]
{37.69911184307752 <- {Rule[a, -1.5], Rule[b, 1.5]}26.729786441110512 <- {Rule[a, -1.5], Rule[b, 0.5]} |
| 19.30.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \pderiv{s}{(1/k)} = \sqrt{a^{2}-b^{2}}\incellintFk@{\phi}{k}} | subs( temp=(1/ k), diff( s, temp$(1) ) ) = sqrt((a)^(2)- (b)^(2))*EllipticF(sin(phi), k) |
(D[s, {temp, 1}]/.temp-> (1/ k)) == Sqrt[(a)^(2)- (b)^(2)]*EllipticF[\[Phi], (k)^2] |
Failure | Failure | Successful [Tested: 300] | Failed [20 / 300]
{Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 1], Rule[s, -1.5], Rule[ϕ, -2]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 1], Rule[s, -1.5], Rule[ϕ, 2]} |
| 19.30.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sqrt{a^{2}-b^{2}}\incellintFk@{\phi}{k} = \sqrt{a^{2}-b^{2}}\CarlsonsymellintRF@{c-1}{c-k^{2}}{c}} | sqrt((a)^(2)- (b)^(2))*EllipticF(sin(phi), k) = sqrt((a)^(2)- (b)^(2))*0.5*int(1/(sqrt(t+c - 1)*sqrt(t+c - (k)^(2))*sqrt(t+c)), t = 0..infinity) |
Sqrt[(a)^(2)- (b)^(2)]*EllipticF[\[Phi], (k)^2] == Sqrt[(a)^(2)- (b)^(2)]*EllipticF[ArcCos[Sqrt[c - 1/c]],(c-c - (k)^(2))/(c-c - 1)]/Sqrt[c-c - 1] |
Error | Failure | Skip - symbolical successful subtest | Skip - No test values generated |
| 19.30#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x = a\sqrt{t+1}} | x = a*sqrt(t + 1) |
x == a*Sqrt[t + 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.30#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle y = b\sqrt{t}} | y = b*sqrt(t) |
y == b*Sqrt[t] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.30.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s = \frac{1}{2}\int_{0}^{y^{2}/b^{2}}\sqrt{\frac{(a^{2}+b^{2})t+b^{2}}{t(t+1)}}\diff{t}} | s = (1)/(2)*int(sqrt((((a)^(2)+ (b)^(2))* t + (b)^(2))/(t*(t + 1))), t = 0..(y)^(2)/ (b)^(2)) |
s == Divide[1,2]*Integrate[Sqrt[Divide[((a)^(2)+ (b)^(2))* t + (b)^(2),t*(t + 1)]], {t, 0, (y)^(2)/ (b)^(2)}, GenerateConditions->None] |
Failure | Aborted | Failed [300 / 300] 300/300]: [[-3.149531120 <- {a = -3/2, b = -3/2, s = -3/2, y = -3/2}-3.149531120 <- {a = -3/2, b = -3/2, s = -3/2, y = 3/2} |
Skipped - Because timed out |
| 19.30.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s = \tfrac{1}{2}I(\mathbf{e}_{1})} | s = (1)/(2)*I*(e[1]) |
s == Divide[1,2]*I*(Subscript[e, 1]) |
Failure | Failure | Failed [298 / 300] 298/300]: [[-1.750000000-.4330127020*I <- {I = 1/2*3^(1/2)+1/2*I, s = -3/2, e[1] = 1/2*3^(1/2)+1/2*I}-1.066987298-.2500000002*I <- {I = 1/2*3^(1/2)+1/2*I, s = -3/2, e[1] = -1/2+1/2*I*3^(1/2)} |
Failed [180 / 180]
{Complex[-1.375, -0.21650635094610968] <- {Rule[Complex[0, 1], 1], Rule[s, -1.5], Rule[Subscript[e, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.375, -0.21650635094610968] <- {Rule[Complex[0, 1], 2], Rule[s, -1.5], Rule[Subscript[e, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.30.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tfrac{1}{2}I(\mathbf{e}_{1}) = -\tfrac{1}{3}a^{2}b^{2}\CarlsonsymellintRD@{r}{r+b^{2}+a^{2}}{r+b^{2}}+y\sqrt{\frac{r+b^{2}+a^{2}}{r+b^{2}}}} | Error |
Divide[1,2]*I*(Subscript[e, 1]) == -Divide[1,3]*(a)^(2)* (b)^(2)* 3*(EllipticF[ArcCos[Sqrt[r/r + (b)^(2)]],(r + (b)^(2)-r + (b)^(2)+ (a)^(2))/(r + (b)^(2)-r)]-EllipticE[ArcCos[Sqrt[r/r + (b)^(2)]],(r + (b)^(2)-r + (b)^(2)+ (a)^(2))/(r + (b)^(2)-r)])/((r + (b)^(2)-r + (b)^(2)+ (a)^(2))*(r + (b)^(2)-r)^(1/2))+ y*Sqrt[Divide[r + (b)^(2)+ (a)^(2),r + (b)^(2)]] |
Missing Macro Error | Failure | Skip - symbolical successful subtest | Skip - No test values generated |
| 19.30.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r^{2} = 2a^{2}\cos@{2\theta}} | (r)^(2) = 2*(a)^(2)* cos(2*theta) |
(r)^(2) == 2*(a)^(2)* Cos[2*\[Theta]] |
Failure | Failure | Failed [108 / 108] 108/108]: [[6.704966234 <- {a = -3/2, r = -3/2, theta = 3/2}-.181360376 <- {a = -3/2, r = -3/2, theta = 1/2} |
Failed [108 / 108]
{6.704966234702004 <- {Rule[a, -1.5], Rule[r, -1.5], Rule[θ, 1.5]}-0.18136037640662916 <- {Rule[a, -1.5], Rule[r, -1.5], Rule[θ, 0.5]} |
| 19.30.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s = 2a^{2}\int_{0}^{r}\frac{\diff{t}}{\sqrt{4a^{4}-t^{4}}}} | s = 2*(a)^(2)* int((1)/(sqrt(4*(a)^(4)- (t)^(4))), t = 0..r) |
s == 2*(a)^(2)* Integrate[Divide[1,Sqrt[4*(a)^(4)- (t)^(4)]], {t, 0, r}, GenerateConditions->None] |
Error | Failure | - | Failed [208 / 216]
{0.042085201578189846 <- {Rule[a, -1.5], Rule[r, -1.5], Rule[s, -1.5]}3.04208520157819 <- {Rule[a, -1.5], Rule[r, -1.5], Rule[s, 1.5]} |
| 19.30.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2a^{2}\int_{0}^{r}\frac{\diff{t}}{\sqrt{4a^{4}-t^{4}}} = \sqrt{2a^{2}}\CarlsonsymellintRF@{q-1}{q}{q+1}} | 2*(a)^(2)* int((1)/(sqrt(4*(a)^(4)- (t)^(4))), t = 0..r) = sqrt(2*(a)^(2))*0.5*int(1/(sqrt(t+q - 1)*sqrt(t+q)*sqrt(t+q + 1)), t = 0..infinity) |
2*(a)^(2)* Integrate[Divide[1,Sqrt[4*(a)^(4)- (t)^(4)]], {t, 0, r}, GenerateConditions->None] == Sqrt[2*(a)^(2)]*EllipticF[ArcCos[Sqrt[q - 1/q + 1]],(q + 1-q)/(q + 1-q - 1)]/Sqrt[q + 1-q - 1] |
Error | Failure | - | Failed [12 / 12]
{Indeterminate <- {Rule[a, -1.5], Rule[q, 2], Rule[r, -1.5]}Indeterminate <- {Rule[a, -1.5], Rule[q, 2], Rule[r, 1.5]} |
| 19.30.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle s = a\incellintFk@{\phi}{1/\sqrt{2}}} | s = a*EllipticF(sin(phi), 1/(sqrt(2))) |
s == a*EllipticF[\[Phi], (1/(Sqrt[2]))^2] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.201379324+.8785912788*I <- {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, s = -3/2}2.798620676+.8785912788*I <- {a = -3/2, phi = 1/2*3^(1/2)+1/2*I, s = 3/2} |
Failed [300 / 300]
{Complex[-0.8505476575870029, 0.390685462269601] <- {Rule[a, -1.5], Rule[s, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.859414812385125, 0.6494166239344216] <- {Rule[a, -1.5], Rule[s, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.30.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle P = 4\sqrt{2a^{2}}\CarlsonsymellintRF@{0}{1}{2}} | P = 4*sqrt(2*(a)^(2))*0.5*int(1/(sqrt(t+0)*sqrt(t+1)*sqrt(t+2)), t = 0..infinity) |
P == 4*Sqrt[2*(a)^(2)]*EllipticF[ArcCos[Sqrt[0/2]],(2-1)/(2-0)]/Sqrt[2-0] |
Failure | Failure | Failed [60 / 60] 60/60]: [[-10.25842266+.5000000000*I <- {P = 1/2*3^(1/2)+1/2*I, a = -3/2}-10.25842266+.5000000000*I <- {P = 1/2*3^(1/2)+1/2*I, a = 3/2} |
Failed [60 / 60]
{Complex[-10.691435361916012, 0.24999999999999997] <- {Rule[a, -1.5], Rule[P, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-11.37444806380823, 0.43301270189221935] <- {Rule[a, -1.5], Rule[P, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.32.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(p) = \CarlsonsymellintRF@{p-x_{1}}{p-x_{2}}{p-x_{3}}} | (x + y*I)*(p) = 0.5*int(1/(sqrt(t+p - x[1])*sqrt(t+p - x[2])*sqrt(t+p - x[3])), t = 0..infinity) |
(x + y*I)*(p) == EllipticF[ArcCos[Sqrt[p - Subscript[x, 1]/p - Subscript[x, 3]]],(p - Subscript[x, 3]-p - Subscript[x, 2])/(p - Subscript[x, 3]-p - Subscript[x, 1])]/Sqrt[p - Subscript[x, 3]-p - Subscript[x, 1]] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Complex[-0.7208699572238464, -0.7193085577979393] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[1.3758216901446034, -2.446030868401005] <- {Rule[p, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.32.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle x_{1} > x_{2}} | x[1] > x[2] |
Subscript[x, 1] > Subscript[x, 2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.32#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(\infty) = 0} | z*(infinity) = 0 |
z*(Infinity) == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.32#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(x_{2}) = z(x_{1})+z(x_{3})} | (x + y*I)*(x[2]) = (x + y*I)*(x[1])+(x + y*I)*(x[3]) |
(x + y*I)*(Subscript[x, 2]) == (x + y*I)*(Subscript[x, 1])+(x + y*I)*(Subscript[x, 3]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.32#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(x_{3}) = \CarlsonsymellintRF@{x_{3}-x_{1}}{x_{3}-x_{2}}{0}} | (x + y*I)*(x[3]) = 0.5*int(1/(sqrt(t+x[3]- x[1])*sqrt(t+x[3]- x[2])*sqrt(t+0)), t = 0..infinity) |
(x + y*I)*(Subscript[x, 3]) == EllipticF[ArcCos[Sqrt[Subscript[x, 3]- Subscript[x, 1]/0]],(0-Subscript[x, 3]- Subscript[x, 2])/(0-Subscript[x, 3]- Subscript[x, 1])]/Sqrt[0-Subscript[x, 3]- Subscript[x, 1]] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Plus[Complex[1.024519052838329, -0.27451905283832906], Times[Complex[-0.25881904510252074, -0.9659258262890683], EllipticF[DirectedInfinity[], 1.0]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Plus[Complex[0.27451905283832917, 1.0245190528383288], Times[Complex[-0.7239434227163943, -0.9434614369855119], EllipticF[DirectedInfinity[], 1.0]]] <- {Rule[x, 1.5], Rule[y, -1.5], Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.32#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{x_{3}-x_{1}}{x_{3}-x_{2}}{0} = -i\CarlsonsymellintRF@{0}{x_{1}-x_{3}}{x_{2}-x_{3}}} | 0.5*int(1/(sqrt(t+x[3]- x[1])*sqrt(t+x[3]- x[2])*sqrt(t+0)), t = 0..infinity) = - I*0.5*int(1/(sqrt(t+0)*sqrt(t+x[1]- x[3])*sqrt(t+x[2]- x[3])), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[Subscript[x, 3]- Subscript[x, 1]/0]],(0-Subscript[x, 3]- Subscript[x, 2])/(0-Subscript[x, 3]- Subscript[x, 1])]/Sqrt[0-Subscript[x, 3]- Subscript[x, 1]] == - I*EllipticF[ArcCos[Sqrt[0/Subscript[x, 2]- Subscript[x, 3]]],(Subscript[x, 2]- Subscript[x, 3]-Subscript[x, 1]- Subscript[x, 3])/(Subscript[x, 2]- Subscript[x, 3]-0)]/Sqrt[Subscript[x, 2]- Subscript[x, 3]-0] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Indeterminate <- {Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Plus[Complex[-0.4754994064110389, 1.6461555153586378], Times[Complex[0.7239434227163943, 0.9434614369855119], EllipticF[DirectedInfinity[], 1.0]]] <- {Rule[Subscript[x, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[x, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.33.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle S = 3V\CarlsonsymellintRG@{a^{-2}}{b^{-2}}{c^{-2}}} | Error |
S == 3*V*Sqrt[(c)^(- 2)-(a)^(- 2)]*(EllipticE[ArcCos[Sqrt[(a)^(- 2)/(c)^(- 2)]],((c)^(- 2)-(b)^(- 2))/((c)^(- 2)-(a)^(- 2))]+(Cot[ArcCos[Sqrt[(a)^(- 2)/(c)^(- 2)]]])^2*EllipticF[ArcCos[Sqrt[(a)^(- 2)/(c)^(- 2)]],((c)^(- 2)-(b)^(- 2))/((c)^(- 2)-(a)^(- 2))]+Cot[ArcCos[Sqrt[(a)^(- 2)/(c)^(- 2)]]]*Sqrt[1-k^2*Sin[ArcCos[Sqrt[(a)^(- 2)/(c)^(- 2)]]]^2]) |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[S, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[V, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[S, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[V, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.33.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{S}{2\pi} = c^{2}+\frac{ab}{\sin@@{\phi}}\left(\incellintEk@{\phi}{k}\sin^{2}@@{\phi}+\incellintFk@{\phi}{k}\cos^{2}@@{\phi}\right)} | (S)/(2*Pi) = (c)^(2)+(a*b)/(sin(phi))*(EllipticE(sin(phi), k)*(sin(phi))^(2)+ EllipticF(sin(phi), k)*(cos(phi))^(2)) |
Divide[S,2*Pi] == (c)^(2)+Divide[a*b,Sin[\[Phi]]]*(EllipticE[\[Phi], (k)^2]*(Sin[\[Phi]])^(2)+ EllipticF[\[Phi], (k)^2]*(Cos[\[Phi]])^(2)) |
Failure | Failure | Failed [300 / 300] 300/300]: [[-4.910443424-.9759333290e-1*I <- {S = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, c = -3/2, phi = 1/2*3^(1/2)+1/2*I, k = 1}-5.505002077-.4622644670e-1*I <- {S = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, c = -3/2, phi = 1/2*3^(1/2)+1/2*I, k = 2} |
Failed [300 / 300]
{Complex[-4.54039506540302, -0.09283854764917886] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[k, 1], Rule[S, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-4.634568996487559, -0.31545051747139075] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[k, 2], Rule[S, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]} |
| 19.33#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@@{\phi} = \frac{c}{a}} | cos(phi) = (c)/(a) |
Cos[\[Phi]] == Divide[c,a] |
Failure | Failure | Failed [300 / 300] 300/300]: [[-.2694569811-.3969495503*I <- {a = -3/2, c = -3/2, phi = 1/2*3^(1/2)+1/2*I}.227765517+.4690753764*I <- {a = -3/2, c = -3/2, phi = -1/2+1/2*I*3^(1/2)} |
Failed [300 / 300]
{Complex[-0.06378043051909243, -0.10599798465255418] <- {Rule[a, -1.5], Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.061176166972244816, 0.11050836582743673] <- {Rule[a, -1.5], Rule[c, -1.5], Rule[ϕ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.33#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k^{2} = \frac{a^{2}(b^{2}-c^{2})}{b^{2}(a^{2}-c^{2})}} | (k)^(2) = ((a)^(2)*((b)^(2)- (c)^(2)))/((b)^(2)*((a)^(2)- (c)^(2))) |
(k)^(2) == Divide[(a)^(2)*((b)^(2)- (c)^(2)),(b)^(2)*((a)^(2)- (c)^(2))] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.33.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{x^{2}}{a^{2}+\lambda}+\frac{y^{2}}{b^{2}+\lambda}+\frac{z^{2}}{c^{2}+\lambda} = 1} | ((x)^(2))/((a)^(2)+ lambda)+((y)^(2))/((b)^(2)+ lambda)+((x + y*I)^(2))/((c)^(2)+ lambda) = 1 |
Divide[(x)^(2),(a)^(2)+ \[Lambda]]+Divide[(y)^(2),(b)^(2)+ \[Lambda]]+Divide[(x + y*I)^(2),(c)^(2)+ \[Lambda]] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.33.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle V(\lambda) = Q\CarlsonsymellintRF@{a^{2}+\lambda}{b^{2}+\lambda}{c^{2}+\lambda}} | V*(lambda) = Q*0.5*int(1/(sqrt(t+(a)^(2)+ lambda)*sqrt(t+(b)^(2)+ lambda)*sqrt(t+(c)^(2)+ lambda)), t = 0..infinity) |
V*(\[Lambda]) == Q*EllipticF[ArcCos[Sqrt[(a)^(2)+ \[Lambda]/(c)^(2)+ \[Lambda]]],((c)^(2)+ \[Lambda]-(b)^(2)+ \[Lambda])/((c)^(2)+ \[Lambda]-(a)^(2)+ \[Lambda])]/Sqrt[(c)^(2)+ \[Lambda]-(a)^(2)+ \[Lambda]] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Complex[-0.01914487900157147, 0.6670953471925876] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[Q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[V, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.08207662518407155, 0.5134467292285442] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[Q, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[V, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[λ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.33.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1/C = \CarlsonsymellintRF@{a^{2}}{b^{2}}{c^{2}}} | 1/ C = 0.5*int(1/(sqrt(t+(a)^(2))*sqrt(t+(b)^(2))*sqrt(t+(c)^(2))), t = 0..infinity) |
1/ C == EllipticF[ArcCos[Sqrt[(a)^(2)/(c)^(2)]],((c)^(2)-(b)^(2))/((c)^(2)-(a)^(2))]/Sqrt[(c)^(2)-(a)^(2)] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[C, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[C, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.33.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L_{c} = 2\pi abc\int_{0}^{\infty}\frac{\diff{\lambda}}{\sqrt{(a^{2}+\lambda)(b^{2}+\lambda)(c^{2}+\lambda)^{3}}}} | L[c] = 2*Pi*a*b*c*int((1)/(sqrt(((a)^(2)+ lambda)*((b)^(2)+ lambda)*((c)^(2)+ lambda)^(3))), lambda = 0..infinity) |
Subscript[L, c] == 2*Pi*a*b*c*Integrate[Divide[1,Sqrt[((a)^(2)+ \[Lambda])*((b)^(2)+ \[Lambda])*((c)^(2)+ \[Lambda])^(3)]], {\[Lambda], 0, Infinity}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.33.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\pi abc\int_{0}^{\infty}\frac{\diff{\lambda}}{\sqrt{(a^{2}+\lambda)(b^{2}+\lambda)(c^{2}+\lambda)^{3}}} = V\CarlsonsymellintRD@{a^{2}}{b^{2}}{c^{2}}} | Error |
2*Pi*a*b*c*Integrate[Divide[1,Sqrt[((a)^(2)+ \[Lambda])*((b)^(2)+ \[Lambda])*((c)^(2)+ \[Lambda])^(3)]], {\[Lambda], 0, Infinity}, GenerateConditions->None] == V*3*(EllipticF[ArcCos[Sqrt[(a)^(2)/(c)^(2)]],((c)^(2)-(b)^(2))/((c)^(2)-(a)^(2))]-EllipticE[ArcCos[Sqrt[(a)^(2)/(c)^(2)]],((c)^(2)-(b)^(2))/((c)^(2)-(a)^(2))])/(((c)^(2)-(b)^(2))*((c)^(2)-(a)^(2))^(1/2)) |
Missing Macro Error | Aborted | Skip - symbolical successful subtest | Skipped - Because timed out |
| 19.33.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle L_{a}+L_{b}+L_{c} = 4\pi} | L[a]+ L[b]+ L[c] = 4*Pi |
Subscript[L, a]+ Subscript[L, b]+ Subscript[L, c] == 4*Pi |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.34.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle ab\int_{0}^{2\pi}(h^{2}+a^{2}+b^{2}-2ab\cos@@{\theta})^{-1/2}\cos@@{\theta}\diff{\theta} = 2ab\int_{-1}^{1}\frac{t\diff{t}}{\sqrt{(1+t)(1-t)(a_{3}-2abt)}}} | a*b*int(((h)^(2)+ (a)^(2)+ (b)^(2)- 2*a*b*cos(theta))^(- 1/ 2)* cos(theta), theta = 0..2*Pi) = 2*a*b*int((t)/(sqrt((1 + t)*(1 - t)*(a[3]- 2*a*b*t))), t = - 1..1) |
a*b*Integrate[((h)^(2)+ (a)^(2)+ (b)^(2)- 2*a*b*Cos[\[Theta]])^(- 1/ 2)* Cos[\[Theta]], {\[Theta], 0, 2*Pi}, GenerateConditions->None] == 2*a*b*Integrate[Divide[t,Sqrt[(1 + t)*(1 - t)*(Subscript[a, 3]- 2*a*b*t)]], {t, - 1, 1}, GenerateConditions->None] |
Aborted | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 19.34.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2ab\int_{-1}^{1}\frac{t\diff{t}}{\sqrt{(1+t)(1-t)(a_{3}-2abt)}} = 2abI(\mathbf{e}_{5})} | 2*a*b*int((t)/(sqrt((1 + t)*(1 - t)*(a[3]- 2*a*b*t))), t = - 1..1) = 2*a*b*I*(e[5]) |
2*a*b*Integrate[Divide[t,Sqrt[(1 + t)*(1 - t)*(Subscript[a, 3]- 2*a*b*t)]], {t, - 1, 1}, GenerateConditions->None] == 2*a*b*I*(Subscript[e, 5]) |
Failure | Aborted | Failed [300 / 300] 300/300]: [[-3.959693187-6.593729744*I <- {I = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, a[3] = 1/2*3^(1/2)+1/2*I, e[5] = 1/2*3^(1/2)+1/2*I}2.187421133-4.946615428*I <- {I = 1/2*3^(1/2)+1/2*I, a = -3/2, b = -3/2, a[3] = 1/2*3^(1/2)+1/2*I, e[5] = -1/2+1/2*I*3^(1/2)} |
Skipped - Because timed out |
| 19.34#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{3} = h^{2}+a^{2}+b^{2}} | a[3] = (h)^(2)+ (a)^(2)+ (b)^(2) |
Subscript[a, 3] == (h)^(2)+ (a)^(2)+ (b)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.34#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{5} = 0} | a[5] = 0 |
Subscript[a, 5] == 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.34#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{5} = 1} | b[5] = 1 |
Subscript[b, 5] == 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.34.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2abI(\mathbf{e}_{5}) = a_{3}I(\boldsymbol{{0}})-I(\mathbf{e}_{3})} | 2*a*b*I*(e[5]) = a[3]*I*(0)- I*(e[3]) |
2*a*b*I*(Subscript[e, 5]) == Subscript[a, 3]*I*(0)- I*(Subscript[e, 3]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.34.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r_{+}^{2} = a_{3}+ 2ab} | (r[+])^(2) = a[3]+ 2*a*b |
(Subscript[r, +])^(2) == Subscript[a, 3]+ 2*a*b |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{1}{2}{4} = \CarlsonsymellintRF@{z_{1}}{z_{2}}{z_{3}}} | 0.5*int(1/(sqrt(t+1)*sqrt(t+2)*sqrt(t+4)), t = 0..infinity) = 0.5*int(1/(sqrt(t+z[1])*sqrt(t+z[2])*sqrt(t+z[3])), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[1/4]],(4-2)/(4-1)]/Sqrt[4-1] == EllipticF[ArcCos[Sqrt[Subscript[z, 1]/Subscript[z, 3]]],(Subscript[z, 3]-Subscript[z, 2])/(Subscript[z, 3]-Subscript[z, 1])]/Sqrt[Subscript[z, 3]-Subscript[z, 1]] |
Aborted | Failure | Skipped - Because timed out | Failed [300 / 300]
{Indeterminate <- {Rule[Subscript[z, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[z, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[z, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.6113291272616378, 0.7460602493090597] <- {Rule[Subscript[z, 1], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[z, 2], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[z, 3], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.36.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \begin{aligned} \displaystyle z_{1}&\displaystyle = 2.10985\;99098\;8,\\ \displaystyle z_{3}&\displaystyle} | |
|
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{1}{2}{4} = 0.68508\;58166\dots} | 0.5*int(1/(sqrt(t+1)*sqrt(t+2)*sqrt(t+4)), t = 0..infinity) = 0.6850858166 |
EllipticF[ArcCos[Sqrt[1/4]],(4-2)/(4-1)]/Sqrt[4-1] == 0.6850858166 |
Failure | Failure | Successful [Tested: 0] | Successful [Tested: 1] |
| 19.36#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2a_{n+1} = a_{n}+\sqrt{a_{n}^{2}-c_{n}^{2}}} | 2*a[n + 1] = sqrt(a(a[n])^(2)- c(c[n])^(2)) |
2*Subscript[a, n + 1] == Sqrt[a(Subscript[a, n])^(2)- c(Subscript[c, n])^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2c_{n+1} = a_{n}-\sqrt{a_{n}^{2}-c_{n}^{2}}} | 2*c[n + 1] = sqrt(a(a[n])^(2)- c(c[n])^(2)) |
2*Subscript[c, n + 1] == Sqrt[a(Subscript[a, n])^(2)- c(Subscript[c, n])^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2t_{n+1} = t_{n}+\sqrt{t_{n}^{2}+\theta c_{n}^{2}}} | 2*t[n + 1] = sqrt(t(t[n])^(2)+ theta*c(c[n])^(2)) |
2*Subscript[t, n + 1] == Sqrt[t(Subscript[t, n])^(2)+ \[Theta]*c(Subscript[c, n])^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 0 < c_{0}} | 0 < c[0] |
0 < Subscript[c, 0] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle t_{0} \geq 0} | t[0] >= 0 |
Subscript[t, 0] >= 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle t_{0}^{2}+\theta a_{0}^{2} \geq 0} | (t[0])^(2)+ theta*(a[0])^(2) >= 0 |
(Subscript[t, 0])^(2)+ \[Theta]*(Subscript[a, 0])^(2) >= 0 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \theta = + 1} | theta = + 1 |
\[Theta] == + 1 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{t_{0}^{2}}{t_{0}^{2}+\theta c_{0}^{2}}{t_{0}^{2}+\theta a_{0}^{2}} = \CarlsonsymellintRF@{T^{2}}{T^{2}}{T^{2}+\theta M^{2}}} | 0.5*int(1/(sqrt(t+t(t[0])^(2))*sqrt(t+t(t[0])^(2)+ theta*c(c[0])^(2))*sqrt(t+t(t[0])^(2)+ theta*a(a[0])^(2))), t = 0..infinity) = 0.5*int(1/(sqrt(t+(T)^(2))*sqrt(t+(T)^(2))*sqrt(t+(T)^(2)+ theta*(M)^(2))), t = 0..infinity) |
EllipticF[ArcCos[Sqrt[t(Subscript[t, 0])^(2)/t(Subscript[t, 0])^(2)+ \[Theta]*a(Subscript[a, 0])^(2)]],(t(Subscript[t, 0])^(2)+ \[Theta]*a(Subscript[a, 0])^(2)-t(Subscript[t, 0])^(2)+ \[Theta]*c(Subscript[c, 0])^(2))/(t(Subscript[t, 0])^(2)+ \[Theta]*a(Subscript[a, 0])^(2)-t(Subscript[t, 0])^(2))]/Sqrt[t(Subscript[t, 0])^(2)+ \[Theta]*a(Subscript[a, 0])^(2)-t(Subscript[t, 0])^(2)] == EllipticF[ArcCos[Sqrt[(T)^(2)/(T)^(2)+ \[Theta]*(M)^(2)]],((T)^(2)+ \[Theta]*(M)^(2)-(T)^(2))/((T)^(2)+ \[Theta]*(M)^(2)-(T)^(2))]/Sqrt[(T)^(2)+ \[Theta]*(M)^(2)-(T)^(2)] |
Error | Failure | - | Failed [300 / 300] {Plus[Complex[0.041390391732804066, 0.9969018367602411], Times[2.8284271247461903, Power[Times[Complex[0.0, 1.0], a], Rational[-1, 2]], EllipticF[ArcCos[Power[Plus[Complex[-0.031249999999999986, 0.05412658773652742], Times[Complex[0.0, 0.125], a]], Rational[1, 2]]], Times[Complex[0.0, -8.0], Power[a, -1], Plus[Times[Complex[0.0, 0.125], a], Times[Complex[0.0, 0.125], c]]]]]] <- {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[a, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[c, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[Subscript[t, 0], Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Plus[Complex[0.041390391732804066, 0.9969018367602411], Times[2.8284
|
| 19.36.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{T^{2}}{T^{2}}{T^{2}+\theta M^{2}} = \CarlsonellintRC@{T^{2}+\theta M^{2}}{T^{2}}} | Error |
EllipticF[ArcCos[Sqrt[(T)^(2)/(T)^(2)+ \[Theta]*(M)^(2)]],((T)^(2)+ \[Theta]*(M)^(2)-(T)^(2))/((T)^(2)+ \[Theta]*(M)^(2)-(T)^(2))]/Sqrt[(T)^(2)+ \[Theta]*(M)^(2)-(T)^(2)] == 1/Sqrt[(T)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((T)^(2)+ \[Theta]*(M)^(2))/((T)^(2))] |
Missing Macro Error | Failure | - | Failed [300 / 300]
{Complex[-1.634056915706757, -0.008820605997006181] <- {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-1.6914869520542948, 0.13073697514602478] <- {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[θ, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.36#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{3}^{2} = 2.46209\;30206\;0} | (a[3])^(2) = 2.46209302060 |
(Subscript[a, 3])^(2) == 2.46209302060 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36#Ex10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle t_{3}^{2} = 1.46971\;53173\;1} | (t[3])^(2) = 1.46971531731 |
(Subscript[t, 3])^(2) == 1.46971531731 |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{1}{2}{4} = \CarlsonellintRC@{T^{2}+M^{2}}{T^{2}}} | Error |
EllipticF[ArcCos[Sqrt[1/4]],(4-2)/(4-1)]/Sqrt[4-1] == 1/Sqrt[(T)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((T)^(2)+ (M)^(2))/((T)^(2))] |
Missing Macro Error | Failure | - | Failed [100 / 100]
{Complex[-0.841498016533642, 0.8813735870195429] <- {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[-0.8857105197615976, -2.720699010523131] <- {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.36.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonellintRC@{T^{2}+M^{2}}{T^{2}} = 0.68508\;58166} | Error |
1/Sqrt[(T)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((T)^(2)+ (M)^(2))/((T)^(2))] == 0.6850858166 |
Missing Macro Error | Failure | - | Failed [100 / 100]
{Complex[0.8414980165670778, -0.8813735870195429] <- {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]]}Complex[0.8857105197950335, 2.720699010523131] <- {Rule[M, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]], Rule[T, Times[Rational[1, 2], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]]} |
| 19.36#Ex11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle h_{n} = \sqrt{t_{n}^{2}+\theta a_{n}^{2}}} | sqrt(t(t[n])^(2)+ theta*a(a[n])^(2)) |
Sqrt[t(Subscript[t, n])^(2)+ \[Theta]*a(Subscript[a, n])^(2)] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36#Ex12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle h_{n} = h_{n-1}\frac{t_{n}}{\sqrt{t_{n}^{2}+\theta c_{n}^{2}}}} | h[n] (t[n])/(sqrt(t(t[n])^(2)+ theta*c(c[n])^(2))) |
Subscript[h, n] Divide[Subscript[t, n],Sqrt[t(Subscript[t, n])^(2)+ \[Theta]*c(Subscript[c, n])^(2)]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 19.36.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 2\CarlsonsymellintRG@{t_{0}^{2}}{t_{0}^{2}+\theta c_{0}^{2}}{t_{0}^{2}+\theta a_{0}^{2}} = \left(t_{0}^{2}+\theta\sum_{m=0}^{\infty}2^{m-1}c_{m}^{2}\right)\CarlsonellintRC@{T^{2}+\theta M^{2}}{T^{2}}+h_{0}+\sum_{m=1}^{\infty}2^{m}(h_{m}-h_{m-1})} | Error |
(t(Subscript[t, 0])^(2)+ \[Theta]*Sum[(2)^(m - 1)* c(Subscript[c, m])^(2), {m, 0, Infinity}, GenerateConditions->None])* 1/Sqrt[(T)^(2)]*Hypergeometric2F1[1/2,1/2,3/2,1-((T)^(2)+ \[Theta]*(M)^(2))/((T)^(2))]+ Subscript[h, 0]+ Sum[(2)^(m)*(Subscript[h, m]- Subscript[h, m - 1]), {m, 1, Infinity}, GenerateConditions->None] |
Missing Macro Error | Aborted | - | Failed [1 / 1]
|