Results of Coulomb Functions

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DLMF Formula Maple Mathematica Symbolic
Maple		 Symbolic
Mathematica		 Numeric
Maple		 Numeric
Mathematica
33.2.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{\rho}+\left(1-\frac{2\eta}{\rho}-\frac{\ell(\ell+1)}{\rho^{2}}\right)w = 0} diff(w, [rho$(2)])+(1 -(2*eta)/(rho)-(ell*(ell + 1))/((rho)^(2)))* w = 0 D[w, {\[Rho], 2}]+(1 -Divide[2*\[Eta],\[Rho]]-Divide[\[ScriptL]*(\[ScriptL]+ 1),\[Rho]^(2)])* w == 0 Failure Failure
Failed [300 / 300]
300/300]: [[-11.25833025+5.499999998*I <- {eta = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, w = 1/2*3^(1/2)+1/2*I, ell = 3}
-5.499999998-11.25833025*I <- {eta = 1/2*3^(1/2)+1/2*I, rho = 1/2*3^(1/2)+1/2*I, w = -1/2+1/2*I*3^(1/2), ell = 3}
Failed [294 / 300]
{Complex[-11.258330249197703, 5.5] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 3], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[10.2583302491977, -3.767949192431125] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 3], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
33.4.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle R_{\ell}X_{\ell-1}-T_{\ell}X_{\ell}+R_{\ell+1}X_{\ell+1} = 0} R[ell]*X[ell - 1]- T[ell]*X[ell]+ R[ell + 1]*X[ell + 1] = 0 Subscript[R, \[ScriptL]]*Subscript[X, \[ScriptL]- 1]- Subscript[T, \[ScriptL]]*Subscript[X, \[ScriptL]]+ Subscript[R, \[ScriptL]+ 1]*Subscript[X, \[ScriptL]+ 1] == 0 Skipped - no semantic math Skipped - no semantic math - -
33.5#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \regCoulombF{\ell}@{0}{\rho} = (\pi\rho/2)^{1/2}\BesselJ{\ell+\frac{1}{2}}@{\rho}} CoulombF(ell, 0, rho) = (Pi*rho/ 2)^(1/ 2)* BesselJ(ell +(1)/(2), rho) Error Failure Missing Macro Error Error -
33.5#Ex9 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \regCoulombF{0}@{0}{\rho} = \sin@@{\rho}} CoulombF(0, 0, rho) = sin(rho) Error Successful Missing Macro Error - -
33.5.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2^{\ell}\ell!}{(2\ell+1)!} = \frac{1}{(2\ell+1)!!}} ((2)^(ell)* factorial(ell))/(factorial(2*ell + 1)) = (1)/(doublefactorial(2*ell + 1)) Divide[(2)^\[ScriptL]* (\[ScriptL])!,(2*\[ScriptL]+ 1)!] == Divide[1,(2*\[ScriptL]+ 1)!!] Failure Failure Error
Failed [1 / 1]
{Plus[Times[Power[2.0, ℓ], Factorial[ℓ], Power[Factorial[Plus[1.0, Times[2.0, ℓ]]], -1]], Times[-1.0, Power[Factorial2[Plus[1.0, Times[2.0, ℓ]]], -1]]] <- {}
33.6.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (k+\ell)(k-\ell-1)A_{k}^{\ell} = 2\eta A_{k-1}^{\ell}-A_{k-2}^{\ell}} (k + ell)*(k - ell - 1)* (A[k])^(ell) = 2*eta*(A[k - 1])^(ell)- (A[k - 2])^(ell) (k + \[ScriptL])*(k - \[ScriptL]- 1)* (Subscript[A, k])^\[ScriptL] == 2*\[Eta]*(Subscript[A, k - 1])^\[ScriptL]- (Subscript[A, k - 2])^\[ScriptL] Skipped - no semantic math Skipped - no semantic math - -
33.6.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{k}^{\ell}(\eta) = \dfrac{(-\iunit)^{k-\ell-1}}{(k-\ell-1)!}\*\genhyperF{2}{1}@{\ell+1-k,\ell+1-\iunit\eta}{2\ell+2}{2}} (A[k])^(ell)*(eta) = ((- I)^(k - ell - 1))/(factorial(k - ell - 1))* hypergeom([ell + 1 - k , ell + 1 - I*eta], [2*ell + 2], 2) (Subscript[A, k])^\[ScriptL]*(\[Eta]) == Divide[(- I)^(k - \[ScriptL]- 1),(k - \[ScriptL]- 1)!]* HypergeometricPFQ[{\[ScriptL]+ 1 - k , \[ScriptL]+ 1 - I*\[Eta]}, {2*\[ScriptL]+ 2}, 2] Failure Failure Error
Failed [293 / 300]
{Complex[0.5000000000000001, 0.8660254037844386] <- {Rule[k, 1], Rule[ℓ, 1], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[A, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[0.0, 1.0] <- {Rule[k, 1], Rule[ℓ, 2], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[A, k], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
33.7.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \regCoulombF{\ell}@{\eta}{\rho} = \frac{\rho^{\ell+1}2^{\ell}e^{\iunit\rho-(\pi\eta/2)}}{|\EulerGamma@{\ell+1+\iunit\eta}|}\int_{0}^{1}e^{-2\iunit\rho t}t^{\ell+\iunit\eta}(1-t)^{\ell-\iunit\eta}\diff{t}} CoulombF(ell, eta, rho) = ((rho)^(ell + 1)* (2)^(ell)* exp(I*rho -(Pi*eta/ 2)))/(abs(GAMMA(ell + 1 + I*eta)))*int(exp(- 2*I*rho*t)*(t)^(ell + I*eta)*(1 - t)^(ell - I*eta), t = 0..1) Error Failure Missing Macro Error Error -
33.8#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \regCoulombF{\ell} = +(q^{-1}(u-p)^{2}+q)^{-1/2}} CoulombF(ell, =, +)*((q)^(- 1)*(u - p)^(2)+ q)^(- 1/ 2) Error Translation Error Missing Macro Error - -
33.8#Ex4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \regCoulombF{\ell} = -(q^{-1}(u-p)^{2}+q)^{-1/2}} CoulombF(ell, =, -)*((q)^(- 1)*(u - p)^(2)+ q)^(- 1/ 2) Error Translation Error Missing Macro Error - -
33.9.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{k(k+2\ell+1)}{2k+2\ell+1}a_{k}-2\eta a_{k-1}+\frac{(k-2)(k+2\ell-1)}{2k+2\ell-3}a_{k-2} = 0} (k*(k + 2*ell + 1))/(2*k + 2*ell + 1)*a[k]- 2*eta*a[k - 1]+((k - 2)*(k + 2*ell - 1))/(2*k + 2*ell - 3)*a[k - 2] = 0 Divide[k*(k + 2*\[ScriptL]+ 1),2*k + 2*\[ScriptL]+ 1]*Subscript[a, k]- 2*\[Eta]*Subscript[a, k - 1]+Divide[(k - 2)*(k + 2*\[ScriptL]- 1),2*k + 2*\[ScriptL]- 3]*Subscript[a, k - 2] == 0 Skipped - no semantic math Skipped - no semantic math - -
33.9.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 4\eta^{2}(k-2\ell)b_{k+1}+kb_{k-1}+b_{k-2} = 0} 4*(eta)^(2)*(k - 2*ell)* b[k + 1]+ k*b[k - 1]+ b[k - 2] = 0 4*\[Eta]^(2)*(k - 2*\[ScriptL])* Subscript[b, k + 1]+ k*Subscript[b, k - 1]+ Subscript[b, k - 2] == 0 Skipped - no semantic math Skipped - no semantic math - -
33.12#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{1} = -\tfrac{1}{5}x} B[1] = -(1)/(5)*x Subscript[B, 1] == -Divide[1,5]*x Skipped - no semantic math Skipped - no semantic math - -
33.12#Ex7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{2} = \tfrac{1}{350}(7x^{5}-30x^{2})} B[2] = (1)/(350)*(7*(x)^(5)- 30*(x)^(2)) Subscript[B, 2] == Divide[1,350]*(7*(x)^(5)- 30*(x)^(2)) Skipped - no semantic math Skipped - no semantic math - -
33.12#Ex8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle B_{3} = \tfrac{1}{15750}(264x^{6}-290x^{3}-560)} B[3] = (1)/(15750)*(264*(x)^(6)- 290*(x)^(3)- 560) Subscript[B, 3] == Divide[1,15750]*(264*(x)^(6)- 290*(x)^(3)- 560) Skipped - no semantic math Skipped - no semantic math - -
33.12.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{z} = \left(4\eta^{2}\left(\frac{1-z}{z}\right)+\frac{\ell(\ell+1)}{z^{2}}\right)w} diff(w, [z$(2)]) = (4*(eta)^(2)*((1 - z)/(z))+(ell*(ell + 1))/((z)^(2)))* w D[w, {z, 2}] == (4*\[Eta]^(2)*(Divide[1 - z,z])+Divide[\[ScriptL]*(\[ScriptL]+ 1),(z)^(2)])* w Failure Failure Error
Failed [296 / 300]
{Complex[-3.7320508075688767, 1.5358983848622458] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 1], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-7.196152422706632, 3.535898384862246] <- {Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 2], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
33.14.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{r}+\left(\epsilon+\frac{2}{r}-\frac{\ell(\ell+1)}{r^{2}}\right)w = 0} diff(w, [r$(2)])+(epsilon +(2)/(r)-(ell*(ell + 1))/((r)^(2)))* w = 0 D[w, {r, 2}]+(\[Epsilon]+Divide[2,r]-Divide[\[ScriptL]*(\[ScriptL]+ 1),(r)^(2)])* w == 0 Failure Failure Error
Failed [300 / 300]
{Complex[-1.0584754935143141, -0.611111111111111] <- {Rule[r, Rational[-3, 2]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 1], Rule[ϵ, 1]}
Complex[-0.19245008972987526, -0.11111111111111109] <- {Rule[r, Rational[-3, 2]], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 1], Rule[ϵ, 2]}
33.14#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = -\eta\rho} r = - eta*rho r == - \[Eta]*\[Rho] Skipped - no semantic math Skipped - no semantic math - -
33.14#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \epsilon = 1/\eta^{2}} epsilon = 1/ (eta)^(2) \[Epsilon] == 1/ \[Eta]^(2) Skipped - no semantic math Skipped - no semantic math - -
33.14.E12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A(\epsilon,\ell) = \frac{\EulerGamma@{1+\ell+\kappa}}{\EulerGamma@{\kappa-\ell}}\kappa^{-2\ell-1}} A*(epsilon , ell) = (GAMMA(1 + ell + kappa))/(GAMMA(kappa - ell))*(kappa)^(- 2*ell - 1) A*(\[Epsilon], \[ScriptL]) == Divide[Gamma[1 + \[ScriptL]+ \[Kappa]],Gamma[\[Kappa]- \[ScriptL]]]*\[Kappa]^(- 2*\[ScriptL]- 1) Failure Failure Error
Failed [6 / 6]
{1.4444444444444444 <- {Rule[ℓ, 1], Rule[ϵ, 1], Rule[κ, Rational[3, 2]]}
Complex[2.4444444444444446, 0.0] <- {Rule[ℓ, 1], Rule[ϵ, 2], Rule[κ, Rational[3, 2]]}
33.14.E15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}\phi_{m,\ell}(r)\phi_{n,\ell}(r)\diff{r} = \Kroneckerdelta{m}{n}} int(phi[m , ell]*(r)* phi[n , ell]*(r), r = 0..infinity) = KroneckerDelta[m, n] Integrate[Subscript[\[Phi], m , \[ScriptL]]*(r)* Subscript[\[Phi], n , \[ScriptL]]*(r), {r, 0, Infinity}, GenerateConditions->None] == KroneckerDelta[m, n] Translation Error Translation Error - -
33.19.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{k}-\gamma_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)\epsilon\gamma_{k-2} = 0} gamma[k]- gamma[k - 1]+(1)/(4)*(k - 1)*(k - 2*ell - 2)* epsilon*gamma[k - 2] = 0 Subscript[\[Gamma], k]- Subscript[\[Gamma], k - 1]+Divide[1,4]*(k - 1)*(k - 2*\[ScriptL]- 2)* \[Epsilon]*Subscript[\[Gamma], k - 2] == 0 Skipped - no semantic math Skipped - no semantic math - -
33.19.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle k(k+2\ell+1)\delta_{k}+2\delta_{k-1}+\epsilon\delta_{k-2}+2(2k+2\ell+1)A(\epsilon,\ell)\alpha_{k} = 0} k*(k + 2*ell + 1)* delta[k]+ 2*delta[k - 1]+ epsilon*delta[k - 2]+ 2*(2*k + 2*ell + 1)* A*(epsilon , ell)* alpha[k] = 0 k*(k + 2*\[ScriptL]+ 1)* Subscript[\[Delta], k]+ 2*Subscript[\[Delta], k - 1]+ \[Epsilon]*Subscript[\[Delta], k - 2]+ 2*(2*k + 2*\[ScriptL]+ 1)* A*(\[Epsilon], \[ScriptL])* Subscript[\[Alpha], k] == 0 Skipped - no semantic math Skipped - no semantic math - -
33.19.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{k}-\beta_{k-1}+\tfrac{1}{4}(k-1)(k-2\ell-2)\epsilon\beta_{k-2}+\tfrac{1}{2}(k-1)\epsilon\gamma_{k-2} = 0} beta[k]- beta[k - 1]+(1)/(4)*(k - 1)*(k - 2*ell - 2)* epsilon*beta[k - 2]+(1)/(2)*(k - 1)* epsilon*gamma[k - 2] = 0 Subscript[\[Beta], k]- Subscript[\[Beta], k - 1]+Divide[1,4]*(k - 1)*(k - 2*\[ScriptL]- 2)* \[Epsilon]*Subscript[\[Beta], k - 2]+Divide[1,2]*(k - 1)* \[Epsilon]*Subscript[\[Gamma], k - 2] == 0 Skipped - no semantic math Skipped - no semantic math - -
33.20#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{k,p} = 0} C[k , p] = 0 Subscript[C, k , p] == 0 Skipped - no semantic math Skipped - no semantic math - -
33.20#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle C_{k,p} = \left(-(2\ell+p)C_{k-1,p-2}+C_{k-1,p-3}\right)/(4p)} C[k , p] = (-(2*ell + p)*C[k - 1 , p - 2]+ C[k - 1 , p - 3])/(4*p) Subscript[C, k , p] == (-(2*\[ScriptL]+ p)*Subscript[C, k - 1 , p - 2]+ Subscript[C, k - 1 , p - 3])/(4*p) Skipped - no semantic math Skipped - no semantic math - -
33.22.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{x}+\left({\sf k}^{2}-\frac{2Z}{x}-\frac{\ell(\ell+1)}{x^{2}}\right)w = 0} diff(w, [x$(2)])+((k)^(2)-(2*Z)/(x)-(ell*(ell + 1))/((x)^(2)))* w = 0 D[w, {x, 2}]+((k)^(2)-Divide[2*Z,x]-Divide[\[ScriptL]*(\[ScriptL]+ 1),(x)^(2)])* w == 0 Failure Failure Error
Failed [297 / 300]
{Complex[-0.5704416218017292, -1.0991449828236957] <- {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, Rational[3, 2]], Rule[Z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 1]}
Complex[-2.110042339640732, -1.9880338717125847] <- {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, Rational[3, 2]], Rule[Z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 2]}
33.22#Ex10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = -\eta\rho} r = - eta*rho r == - \[Eta]*\[Rho] Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \epsilon = 1/\eta^{2}} epsilon = 1/ (eta)^(2) \[Epsilon] == 1/ \[Eta]^(2) Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = 2\iunit\rho} z = 2*I*rho z == 2*I*\[Rho] Failure Failure
Failed [70 / 70]
70/70]: [[1.866025404-1.232050808*I <- {rho = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}
.5000000000-.8660254040*I <- {rho = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}
Failed [70 / 70]
{Complex[1.8660254037844386, -1.2320508075688774] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[2.598076211353316, 1.4999999999999996] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
33.22#Ex13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \kappa = \iunit\eta} kappa = I*eta \[Kappa] == I*\[Eta] Failure Failure
Failed [96 / 100]
96/100]: [[1.366025404-.3660254040*I <- {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2*3^(1/2)+1/2*I}
1.000000000-1.732050808*I <- {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2-1/2*I*3^(1/2)}
Failed [96 / 100]
{Complex[1.3660254037844386, -0.36602540378443876] <- {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[1.0, -1.7320508075688772] <- {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}
33.22#Ex14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho = z/(2\iunit)} rho = z/(2*I) \[Rho] == z/(2*I) Failure Failure
Failed [70 / 70]
70/70]: [[.6160254040+.9330127020*I <- {rho = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}
.4330127020+.2500000000*I <- {rho = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}
Failed [70 / 70]
{Complex[0.6160254037844387, 0.9330127018922193] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[-0.7499999999999998, 1.299038105676658] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}
33.22#Ex15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta = \kappa/\iunit} eta = kappa/ I \[Eta] == \[Kappa]/ I Failure Failure
Failed [96 / 100]
96/100]: [[.3660254040+1.366025404*I <- {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2*3^(1/2)+1/2*I}
1.732050808+1.000000000*I <- {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2-1/2*I*3^(1/2)}
Failed [96 / 100]
{Complex[0.36602540378443876, 1.3660254037844386] <- {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Complex[1.7320508075688772, 1.0] <- {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}
33.22#Ex16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = \kappa z/2} r = kappa*z/ 2 r == \[Kappa]*z/ 2 Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex17 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \epsilon = -1/\kappa^{2}} epsilon = - 1/ (kappa)^(2) \[Epsilon] == - 1/ \[Kappa]^(2) Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta = +\epsilon^{-1/2}} eta = + (epsilon)^(- 1/ 2) \[Eta] == + \[Epsilon]^(- 1/ 2) Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho = -r/\eta} rho = - r/ eta \[Rho] == - r/ \[Eta] Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \kappa = +(-\epsilon)^{-1/2}} kappa = +(- epsilon)^(- 1/ 2) \[Kappa] == +(- \[Epsilon])^(- 1/ 2) Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = 2r/\kappa} z = 2*r/ kappa z == 2*r/ \[Kappa] Skipped - no semantic math Skipped - no semantic math - -
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