Results of Theta Functions
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| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 20.2.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{1}@{z}{\tau} = \Jacobithetaq{1}@{z}{q}} | JacobiTheta1(z,exp(I*Pi*tau))= JacobiTheta1(z, q) |
EllipticTheta[1, z, \[Tau]]= EllipticTheta[1, z, q] |
Failure | Failure | Error | Successful |
| 20.2.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{2}@{z}{\tau} = \Jacobithetaq{2}@{z}{q}} | JacobiTheta2(z,exp(I*Pi*tau))= JacobiTheta2(z, q) |
EllipticTheta[2, z, \[Tau]]= EllipticTheta[2, z, q] |
Failure | Failure | Error | Successful |
| 20.2.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{3}@{z}{\tau} = \Jacobithetaq{3}@{z}{q}} | JacobiTheta3(z,exp(I*Pi*tau))= JacobiTheta3(z, q) |
EllipticTheta[3, z, \[Tau]]= EllipticTheta[3, z, q] |
Failure | Failure | Error | Successful |
| 20.2.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{4}@{z}{\tau} = \Jacobithetaq{4}@{z}{q}} | JacobiTheta4(z,exp(I*Pi*tau))= JacobiTheta4(z, q) |
EllipticTheta[4, z, \[Tau]]= EllipticTheta[4, z, q] |
Failure | Failure | Error | Successful |
| 20.2.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{1}@{z+(m+n\tau)\pi}{\tau} = (-1)^{m+n}q^{-n^{2}}e^{-2inz}\Jacobithetatau{1}@{z}{\tau}} | JacobiTheta1(z +(m + n*tau)* Pi,exp(I*Pi*tau))=(- 1)^(m + n)* (q)^(- (n)^(2))* exp(- 2*I*n*z)*JacobiTheta1(z,exp(I*Pi*tau)) |
EllipticTheta[1, z +(m + n*\[Tau])* Pi, \[Tau]]=(- 1)^(m + n)* (q)^(- (n)^(2))* Exp[- 2*I*n*z]*EllipticTheta[1, z, \[Tau]] |
Failure | Failure | Error | Skip |
| 20.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{2}@{z+(m+n\tau)\pi}{\tau} = (-1)^{m}q^{-n^{2}}e^{-2inz}\Jacobithetatau{2}@{z}{\tau}} | JacobiTheta2(z +(m + n*tau)* Pi,exp(I*Pi*tau))=(- 1)^(m)* (q)^(- (n)^(2))* exp(- 2*I*n*z)*JacobiTheta2(z,exp(I*Pi*tau)) |
EllipticTheta[2, z +(m + n*\[Tau])* Pi, \[Tau]]=(- 1)^(m)* (q)^(- (n)^(2))* Exp[- 2*I*n*z]*EllipticTheta[2, z, \[Tau]] |
Failure | Failure | Error | Skip |
| 20.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{3}@{z+(m+n\tau)\pi}{\tau} = q^{-n^{2}}e^{-2inz}\Jacobithetatau{3}@{z}{\tau}} | JacobiTheta3(z +(m + n*tau)* Pi,exp(I*Pi*tau))= (q)^(- (n)^(2))* exp(- 2*I*n*z)*JacobiTheta3(z,exp(I*Pi*tau)) |
EllipticTheta[3, z +(m + n*\[Tau])* Pi, \[Tau]]= (q)^(- (n)^(2))* Exp[- 2*I*n*z]*EllipticTheta[3, z, \[Tau]] |
Failure | Failure | Error | Skip |
| 20.2.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{4}@{z+(m+n\tau)\pi}{\tau} = (-1)^{n}q^{-n^{2}}e^{-2inz}\Jacobithetatau{4}@{z}{\tau}} | JacobiTheta4(z +(m + n*tau)* Pi,exp(I*Pi*tau))=(- 1)^(n)* (q)^(- (n)^(2))* exp(- 2*I*n*z)*JacobiTheta4(z,exp(I*Pi*tau)) |
EllipticTheta[4, z +(m + n*\[Tau])* Pi, \[Tau]]=(- 1)^(n)* (q)^(- (n)^(2))* Exp[- 2*I*n*z]*EllipticTheta[4, z, \[Tau]] |
Failure | Failure | Error | Skip |
| 20.2.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{1}@{z}{\tau} = -\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi}{\tau}} | JacobiTheta1(z,exp(I*Pi*tau))= - JacobiTheta2(z +(1)/(2)*Pi,exp(I*Pi*tau)) |
EllipticTheta[1, z, \[Tau]]= - EllipticTheta[2, z +Divide[1,2]*Pi, \[Tau]] |
Successful | Failure | - | Successful |
| 20.2.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi}{\tau} = -iM\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi\tau}{\tau}} | - JacobiTheta2(z +(1)/(2)*Pi,exp(I*Pi*tau))= - I*M*JacobiTheta4(z +(1)/(2)*Pi*tau,exp(I*Pi*tau)) |
- EllipticTheta[2, z +Divide[1,2]*Pi, \[Tau]]= - I*M*EllipticTheta[4, z +Divide[1,2]*Pi*\[Tau], \[Tau]] |
Failure | Failure | Error | Successful |
| 20.2.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -iM\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi\tau}{\tau} = -iM\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}} | - I*M*JacobiTheta4(z +(1)/(2)*Pi*tau,exp(I*Pi*tau))= - I*M*JacobiTheta3(z +(1)/(2)*Pi +(1)/(2)*Pi*tau,exp(I*Pi*tau)) |
- I*M*EllipticTheta[4, z +Divide[1,2]*Pi*\[Tau], \[Tau]]= - I*M*EllipticTheta[3, z +Divide[1,2]*Pi +Divide[1,2]*Pi*\[Tau], \[Tau]] |
Successful | Failure | - | Successful |
| 20.2.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{2}@{z}{\tau} = \Jacobithetatau{1}@{z+\tfrac{1}{2}\pi}{\tau}} | JacobiTheta2(z,exp(I*Pi*tau))= JacobiTheta1(z +(1)/(2)*Pi,exp(I*Pi*tau)) |
EllipticTheta[2, z, \[Tau]]= EllipticTheta[1, z +Divide[1,2]*Pi, \[Tau]] |
Successful | Failure | - | Successful |
| 20.2.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{1}@{z+\tfrac{1}{2}\pi}{\tau} = M\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi\tau}{\tau}} | JacobiTheta1(z +(1)/(2)*Pi,exp(I*Pi*tau))= M*JacobiTheta3(z +(1)/(2)*Pi*tau,exp(I*Pi*tau)) |
EllipticTheta[1, z +Divide[1,2]*Pi, \[Tau]]= M*EllipticTheta[3, z +Divide[1,2]*Pi*\[Tau], \[Tau]] |
Failure | Failure | Error | Successful |
| 20.2.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M\Jacobithetatau{3}@{z+\tfrac{1}{2}\pi\tau}{\tau} = M\Jacobithetatau{4}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}} | M*JacobiTheta3(z +(1)/(2)*Pi*tau,exp(I*Pi*tau))= M*JacobiTheta4(z +(1)/(2)*Pi +(1)/(2)*Pi*tau,exp(I*Pi*tau)) |
M*EllipticTheta[3, z +Divide[1,2]*Pi*\[Tau], \[Tau]]= M*EllipticTheta[4, z +Divide[1,2]*Pi +Divide[1,2]*Pi*\[Tau], \[Tau]] |
Successful | Failure | - | Successful |
| 20.2.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{3}@{z}{\tau} = \Jacobithetatau{4}@{z+\tfrac{1}{2}\pi}{\tau}} | JacobiTheta3(z,exp(I*Pi*tau))= JacobiTheta4(z +(1)/(2)*Pi,exp(I*Pi*tau)) |
EllipticTheta[3, z, \[Tau]]= EllipticTheta[4, z +Divide[1,2]*Pi, \[Tau]] |
Successful | Failure | - | Successful |
| 20.2.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{4}@{z+\tfrac{1}{2}\pi}{\tau} = M\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi\tau}{\tau}} | JacobiTheta4(z +(1)/(2)*Pi,exp(I*Pi*tau))= M*JacobiTheta2(z +(1)/(2)*Pi*tau,exp(I*Pi*tau)) |
EllipticTheta[4, z +Divide[1,2]*Pi, \[Tau]]= M*EllipticTheta[2, z +Divide[1,2]*Pi*\[Tau], \[Tau]] |
Failure | Failure | Error | Successful |
| 20.2.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi\tau}{\tau} = M\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}} | M*JacobiTheta2(z +(1)/(2)*Pi*tau,exp(I*Pi*tau))= M*JacobiTheta1(z +(1)/(2)*Pi +(1)/(2)*Pi*tau,exp(I*Pi*tau)) |
M*EllipticTheta[2, z +Divide[1,2]*Pi*\[Tau], \[Tau]]= M*EllipticTheta[1, z +Divide[1,2]*Pi +Divide[1,2]*Pi*\[Tau], \[Tau]] |
Successful | Failure | - | Successful |
| 20.2.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{4}@{z}{\tau} = \Jacobithetatau{3}@{z+\tfrac{1}{2}\pi}{\tau}} | JacobiTheta4(z,exp(I*Pi*tau))= JacobiTheta3(z +(1)/(2)*Pi,exp(I*Pi*tau)) |
EllipticTheta[4, z, \[Tau]]= EllipticTheta[3, z +Divide[1,2]*Pi, \[Tau]] |
Successful | Failure | - | Successful |
| 20.2.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{3}@{z+\tfrac{1}{2}\pi}{\tau} = -iM\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi\tau}{\tau}} | JacobiTheta3(z +(1)/(2)*Pi,exp(I*Pi*tau))= - I*M*JacobiTheta1(z +(1)/(2)*Pi*tau,exp(I*Pi*tau)) |
EllipticTheta[3, z +Divide[1,2]*Pi, \[Tau]]= - I*M*EllipticTheta[1, z +Divide[1,2]*Pi*\[Tau], \[Tau]] |
Failure | Failure | Error | Successful |
| 20.2.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -iM\Jacobithetatau{1}@{z+\tfrac{1}{2}\pi\tau}{\tau} = iM\Jacobithetatau{2}@{z+\tfrac{1}{2}\pi+\tfrac{1}{2}\pi\tau}{\tau}} | - I*M*JacobiTheta1(z +(1)/(2)*Pi*tau,exp(I*Pi*tau))= I*M*JacobiTheta2(z +(1)/(2)*Pi +(1)/(2)*Pi*tau,exp(I*Pi*tau)) |
- I*M*EllipticTheta[1, z +Divide[1,2]*Pi*\[Tau], \[Tau]]= I*M*EllipticTheta[2, z +Divide[1,2]*Pi +Divide[1,2]*Pi*\[Tau], \[Tau]] |
Successful | Failure | - | Successful |
| 20.4.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{1}@{0}{q} = \Jacobithetaq{2}'@{0}{q}} | JacobiTheta1(0, q)= subs( temp=0, diff( JacobiTheta2(temp, q), temp$(1) ) ) |
EllipticTheta[1, 0, q]= (D[EllipticTheta[2, temp, q], {temp, 1}]/.temp-> 0) |
Successful | Successful | - | - |
| 20.4.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{2}'@{0}{q} = \Jacobithetaq{3}'@{0}{q}} | subs( temp=0, diff( JacobiTheta2(temp, q), temp$(1) ) )= subs( temp=0, diff( JacobiTheta3(temp, q), temp$(1) ) ) |
(D[EllipticTheta[2, temp, q], {temp, 1}]/.temp-> 0)= (D[EllipticTheta[3, temp, q], {temp, 1}]/.temp-> 0) |
Failure | Successful | Error | - |
| 20.4.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{3}'@{0}{q} = \Jacobithetaq{4}'@{0}{q}} | subs( temp=0, diff( JacobiTheta3(temp, q), temp$(1) ) )= subs( temp=0, diff( JacobiTheta4(temp, q), temp$(1) ) ) |
(D[EllipticTheta[3, temp, q], {temp, 1}]/.temp-> 0)= (D[EllipticTheta[4, temp, q], {temp, 1}]/.temp-> 0) |
Failure | Successful | Skip | - |
| 20.4.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{4}'@{0}{q} = 0} | subs( temp=0, diff( JacobiTheta4(temp, q), temp$(1) ) )= 0 |
(D[EllipticTheta[4, temp, q], {temp, 1}]/.temp-> 0)= 0 |
Successful | Successful | - | - |
| 20.4.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{1}'@{0}{q} = \Jacobithetaq{2}@{0}{q}\Jacobithetaq{3}@{0}{q}\Jacobithetaq{4}@{0}{q}} | subs( temp=0, diff( JacobiTheta1(temp, q), temp$(1) ) )= JacobiTheta2(0, q)*JacobiTheta3(0, q)*JacobiTheta4(0, q) |
(D[EllipticTheta[1, temp, q], {temp, 1}]/.temp-> 0)= EllipticTheta[2, 0, q]*EllipticTheta[3, 0, q]*EllipticTheta[4, 0, q] |
Failure | Failure | Error | Successful |
| 20.4.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{1}''(0,q) = \Jacobithetaq{2}'''@{0}{q}} | subs( temp=(0 , q), diff( JacobiTheta1(temp, =), temp$(2) ) )*subs( temp=0, diff( JacobiTheta2(temp, q), temp$(3) ) ) |
(D[EllipticTheta[1, temp, =], {temp, 2}]/.temp-> (0 , q))*(D[EllipticTheta[2, temp, q], {temp, 3}]/.temp-> 0) |
Error | Failure | - | Error |
| 20.4.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{2}'''@{0}{q} = \Jacobithetaq{3}'''@{0}{q}} | subs( temp=0, diff( JacobiTheta2(temp, q), temp$(3) ) )= subs( temp=0, diff( JacobiTheta3(temp, q), temp$(3) ) ) |
(D[EllipticTheta[2, temp, q], {temp, 3}]/.temp-> 0)= (D[EllipticTheta[3, temp, q], {temp, 3}]/.temp-> 0) |
Failure | Failure | Error | Fail
Complex[0.0, 2.8284271247461903] <- {Rule[Derivative[0, 2, 0][EllipticThetaPrime][2, 0, q], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Derivative[0, 2, 0][EllipticThetaPrime][3, 0, q], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[2.8284271247461903, 2.8284271247461903] <- {Rule[Derivative[0, 2, 0][EllipticThetaPrime][2, 0, q], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Derivative[0, 2, 0][EllipticThetaPrime][3, 0, q], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}2.8284271247461903 <- {Rule[Derivative[0, 2, 0][EllipticThetaPrime][2, 0, q], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Derivative[0, 2, 0][EllipticThetaPrime][3, 0, q], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -2.8284271247461903] <- {Rule[Derivative[0, 2, 0][EllipticThetaPrime][2, 0, q], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Derivative[0, 2, 0][EllipticThetaPrime][3, 0, q], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 20.4.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{3}'''@{0}{q} = \Jacobithetaq{4}'''@{0}{q}} | subs( temp=0, diff( JacobiTheta3(temp, q), temp$(3) ) )= subs( temp=0, diff( JacobiTheta4(temp, q), temp$(3) ) ) |
(D[EllipticTheta[3, temp, q], {temp, 3}]/.temp-> 0)= (D[EllipticTheta[4, temp, q], {temp, 3}]/.temp-> 0) |
Failure | Failure | Skip | Fail
Complex[0.0, 2.8284271247461903] <- {Rule[Derivative[0, 2, 0][EllipticThetaPrime][3, 0, q], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Derivative[0, 2, 0][EllipticThetaPrime][4, 0, q], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[2.8284271247461903, 2.8284271247461903] <- {Rule[Derivative[0, 2, 0][EllipticThetaPrime][3, 0, q], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Derivative[0, 2, 0][EllipticThetaPrime][4, 0, q], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}2.8284271247461903 <- {Rule[Derivative[0, 2, 0][EllipticThetaPrime][3, 0, q], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[Derivative[0, 2, 0][EllipticThetaPrime][4, 0, q], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, -2.8284271247461903] <- {Rule[Derivative[0, 2, 0][EllipticThetaPrime][3, 0, q], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[Derivative[0, 2, 0][EllipticThetaPrime][4, 0, q], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 20.4.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{4}'''@{0}{q} = 0} | subs( temp=0, diff( JacobiTheta4(temp, q), temp$(3) ) )= 0 |
(D[EllipticTheta[4, temp, q], {temp, 3}]/.temp-> 0)= 0 |
Successful | Failure | - | Fail
Complex[1.4142135623730951, 1.4142135623730951] <- {Rule[Derivative[0, 2, 0][EllipticThetaPrime][4, 0, q], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[1.4142135623730951, -1.4142135623730951] <- {Rule[Derivative[0, 2, 0][EllipticThetaPrime][4, 0, q], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, -1.4142135623730951] <- {Rule[Derivative[0, 2, 0][EllipticThetaPrime][4, 0, q], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}Complex[-1.4142135623730951, 1.4142135623730951] <- {Rule[Derivative[0, 2, 0][EllipticThetaPrime][4, 0, q], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 20.4.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{1}'''@{0}{q}}{\Jacobithetaq{1}'@{0}{q}} = -1+24\sum_{n=1}^{\infty}\frac{q^{2n}}{(1-q^{2n})^{2}}} | (subs( temp=0, diff( JacobiTheta1(temp, q), temp$(3) ) ))/(subs( temp=0, diff( JacobiTheta1(temp, q), temp$(1) ) ))= - 1 + 24*sum(((q)^(2*n))/((1 - (q)^(2*n))^(2)), n = 1..infinity) |
Divide[D[EllipticTheta[1, temp, q], {temp, 3}]/.temp-> 0,D[EllipticTheta[1, temp, q], {temp, 1}]/.temp-> 0]= - 1 + 24*Sum[Divide[(q)^(2*n),(1 - (q)^(2*n))^(2)], {n, 1, Infinity}] |
Failure | Failure | Skip | Skip |
| 20.4.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{2}''@{0}{q}}{\Jacobithetaq{2}@{0}{q}} = -1-8\sum_{n=1}^{\infty}\frac{q^{2n}}{(1+q^{2n})^{2}}} | (subs( temp=0, diff( JacobiTheta2(temp, q), temp$(2) ) ))/(JacobiTheta2(0, q))= - 1 - 8*sum(((q)^(2*n))/((1 + (q)^(2*n))^(2)), n = 1..infinity) |
Divide[D[EllipticTheta[2, temp, q], {temp, 2}]/.temp-> 0,EllipticTheta[2, 0, q]]= - 1 - 8*Sum[Divide[(q)^(2*n),(1 + (q)^(2*n))^(2)], {n, 1, Infinity}] |
Failure | Failure | Skip | Skip |
| 20.4.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{3}''@{0}{q}}{\Jacobithetaq{3}@{0}{q}} = -8\sum_{n=1}^{\infty}\frac{q^{2n-1}}{(1+q^{2n-1})^{2}}} | (subs( temp=0, diff( JacobiTheta3(temp, q), temp$(2) ) ))/(JacobiTheta3(0, q))= - 8*sum(((q)^(2*n - 1))/((1 + (q)^(2*n - 1))^(2)), n = 1..infinity) |
Divide[D[EllipticTheta[3, temp, q], {temp, 2}]/.temp-> 0,EllipticTheta[3, 0, q]]= - 8*Sum[Divide[(q)^(2*n - 1),(1 + (q)^(2*n - 1))^(2)], {n, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 20.4.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{4}''@{0}{q}}{\Jacobithetaq{4}@{0}{q}} = 8\sum_{n=1}^{\infty}\frac{q^{2n-1}}{(1-q^{2n-1})^{2}}} | (subs( temp=0, diff( JacobiTheta4(temp, q), temp$(2) ) ))/(JacobiTheta4(0, q))= 8*sum(((q)^(2*n - 1))/((1 - (q)^(2*n - 1))^(2)), n = 1..infinity) |
Divide[D[EllipticTheta[4, temp, q], {temp, 2}]/.temp-> 0,EllipticTheta[4, 0, q]]= 8*Sum[Divide[(q)^(2*n - 1),(1 - (q)^(2*n - 1))^(2)], {n, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 20.4.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{1}'''@{0}{q}}{\Jacobithetaq{1}'@{0}{q}} = \frac{\Jacobithetaq{2}''@{0}{q}}{\Jacobithetaq{2}@{0}{q}}+\frac{\Jacobithetaq{3}''@{0}{q}}{\Jacobithetaq{3}@{0}{q}}+\frac{\Jacobithetaq{4}''@{0}{q}}{\Jacobithetaq{4}@{0}{q}}} | (subs( temp=0, diff( JacobiTheta1(temp, q), temp$(3) ) ))/(subs( temp=0, diff( JacobiTheta1(temp, q), temp$(1) ) ))=(subs( temp=0, diff( JacobiTheta2(temp, q), temp$(2) ) ))/(JacobiTheta2(0, q))+(subs( temp=0, diff( JacobiTheta3(temp, q), temp$(2) ) ))/(JacobiTheta3(0, q))+(subs( temp=0, diff( JacobiTheta4(temp, q), temp$(2) ) ))/(JacobiTheta4(0, q)) |
Divide[D[EllipticTheta[1, temp, q], {temp, 3}]/.temp-> 0,D[EllipticTheta[1, temp, q], {temp, 1}]/.temp-> 0]=Divide[D[EllipticTheta[2, temp, q], {temp, 2}]/.temp-> 0,EllipticTheta[2, 0, q]]+Divide[D[EllipticTheta[3, temp, q], {temp, 2}]/.temp-> 0,EllipticTheta[3, 0, q]]+Divide[D[EllipticTheta[4, temp, q], {temp, 2}]/.temp-> 0,EllipticTheta[4, 0, q]] |
Failure | Failure | Error | Successful |
| 20.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{1}@{z}{\tau} = \Jacobithetatau{1}'@{0}{\tau}\sin@@{z}\prod_{n=1}^{\infty}\frac{\sin@{n\pi\tau+z}\sin@{n\pi\tau-z}}{\sin^{2}@{n\pi\tau}}} | JacobiTheta1(z,exp(I*Pi*tau))= subs( temp=0, diff( JacobiTheta1(temp,exp(I*Pi*tau)), temp$(1) ) )*sin(z)*product((sin(n*Pi*tau + z)*sin(n*Pi*tau - z))/((sin(n*Pi*tau))^(2)), n = 1..infinity) |
EllipticTheta[1, z, \[Tau]]= (D[EllipticTheta[1, temp, \[Tau]], {temp, 1}]/.temp-> 0)*Sin[z]*Product[Divide[Sin[n*Pi*\[Tau]+ z]*Sin[n*Pi*\[Tau]- z],(Sin[n*Pi*\[Tau]])^(2)], {n, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 20.5.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{2}@{z}{\tau} = \Jacobithetatau{2}@{0}{\tau}\cos@@{z}\prod_{n=1}^{\infty}\frac{\cos@{n\pi\tau+z}\cos@{n\pi\tau-z}}{\cos^{2}@{n\pi\tau}}} | JacobiTheta2(z,exp(I*Pi*tau))= JacobiTheta2(0,exp(I*Pi*tau))*cos(z)*product((cos(n*Pi*tau + z)*cos(n*Pi*tau - z))/((cos(n*Pi*tau))^(2)), n = 1..infinity) |
EllipticTheta[2, z, \[Tau]]= EllipticTheta[2, 0, \[Tau]]*Cos[z]*Product[Divide[Cos[n*Pi*\[Tau]+ z]*Cos[n*Pi*\[Tau]- z],(Cos[n*Pi*\[Tau]])^(2)], {n, 1, Infinity}] |
Failure | Failure | Skip | Skip |
| 20.5.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{3}@{z}{\tau} = \Jacobithetatau{3}@{0}{\tau}\prod_{n=1}^{\infty}\frac{\cos@{(n-\tfrac{1}{2})\pi\tau+z}\cos@{(n-\tfrac{1}{2})\pi\tau-z}}{\cos^{2}@{(n-\tfrac{1}{2})\pi\tau}}} | JacobiTheta3(z,exp(I*Pi*tau))= JacobiTheta3(0,exp(I*Pi*tau))*product((cos((n -(1)/(2))* Pi*tau + z)*cos((n -(1)/(2))* Pi*tau - z))/((cos((n -(1)/(2))* Pi*tau))^(2)), n = 1..infinity) |
EllipticTheta[3, z, \[Tau]]= EllipticTheta[3, 0, \[Tau]]*Product[Divide[Cos[(n -Divide[1,2])* Pi*\[Tau]+ z]*Cos[(n -Divide[1,2])* Pi*\[Tau]- z],(Cos[(n -Divide[1,2])* Pi*\[Tau]])^(2)], {n, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 20.5.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{4}@{z}{\tau} = \Jacobithetatau{4}@{0}{\tau}\prod_{n=1}^{\infty}\frac{\sin@{(n-\tfrac{1}{2})\pi\tau+z}\sin@{(n-\tfrac{1}{2})\pi\tau-z}}{\sin^{2}@{(n-\tfrac{1}{2})\pi\tau}}} | JacobiTheta4(z,exp(I*Pi*tau))= JacobiTheta4(0,exp(I*Pi*tau))*product((sin((n -(1)/(2))* Pi*tau + z)*sin((n -(1)/(2))* Pi*tau - z))/((sin((n -(1)/(2))* Pi*tau))^(2)), n = 1..infinity) |
EllipticTheta[4, z, \[Tau]]= EllipticTheta[4, 0, \[Tau]]*Product[Divide[Sin[(n -Divide[1,2])* Pi*\[Tau]+ z]*Sin[(n -Divide[1,2])* Pi*\[Tau]- z],(Sin[(n -Divide[1,2])* Pi*\[Tau]])^(2)], {n, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 20.5.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=-\infty}^{\infty}p^{2n}q^{n^{2}}\\ = \prod_{n=1}^{\infty}\left(1-q^{2n}\right)\left(1+q^{2n-1}p^{2}\right)\left(1+q^{2n-1}p^{-2}\right)} | sum((p)^(2*n)* (q)^((n)^(2)), n = - infinity..infinity)= product((1 - (q)^(2*n))*(1 + (q)^(2*n - 1)* (p)^(2))*(1 + (q)^(2*n - 1)* (p)^(- 2)), n = 1..infinity) |
Sum[(p)^(2*n)* (q)^((n)^(2)), {n, - Infinity, Infinity}]= Product[(1 - (q)^(2*n))*(1 + (q)^(2*n - 1)* (p)^(2))*(1 + (q)^(2*n - 1)* (p)^(- 2)), {n, 1, Infinity}] |
Error | Error | - | - |
| 20.5.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{1}'@{z}{q}}{\Jacobithetaq{1}@{z}{q}}-\cot@@{z} = 4\sin@{2z}\sum_{n=1}^{\infty}\frac{q^{2n}}{1-2q^{2n}\cos@{2z}+q^{4n}}} | (subs( temp=z, diff( JacobiTheta1(temp, q), temp$(1) ) ))/(JacobiTheta1(z, q))- cot(z)= 4*sin(2*z)*sum(((q)^(2*n))/(1 - 2*(q)^(2*n)* cos(2*z)+ (q)^(4*n)), n = 1..infinity) |
Divide[D[EllipticTheta[1, temp, q], {temp, 1}]/.temp-> z,EllipticTheta[1, z, q]]- Cot[z]= 4*Sin[2*z]*Sum[Divide[(q)^(2*n),1 - 2*(q)^(2*n)* Cos[2*z]+ (q)^(4*n)], {n, 1, Infinity}] |
Failure | Failure | Skip | Skip |
| 20.5.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 4\sin@{2z}\sum_{n=1}^{\infty}\frac{q^{2n}}{1-2q^{2n}\cos@{2z}+q^{4n}} = 4\sum_{n=1}^{\infty}\frac{q^{2n}}{1-q^{2n}}\sin@{2nz}} | 4*sin(2*z)*sum(((q)^(2*n))/(1 - 2*(q)^(2*n)* cos(2*z)+ (q)^(4*n)), n = 1..infinity)= 4*sum(((q)^(2*n))/(1 - (q)^(2*n))*sin(2*n*z), n = 1..infinity) |
4*Sin[2*z]*Sum[Divide[(q)^(2*n),1 - 2*(q)^(2*n)* Cos[2*z]+ (q)^(4*n)], {n, 1, Infinity}]= 4*Sum[Divide[(q)^(2*n),1 - (q)^(2*n)]*Sin[2*n*z], {n, 1, Infinity}] |
Failure | Failure | Skip | Skip |
| 20.5.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{2}'@{z}{q}}{\Jacobithetaq{2}@{z}{q}}+\tan@@{z} = -4\sin@{2z}\sum_{n=1}^{\infty}\frac{q^{2n}}{1+2q^{2n}\cos@{2z}+q^{4n}}} | (subs( temp=z, diff( JacobiTheta2(temp, q), temp$(1) ) ))/(JacobiTheta2(z, q))+ tan(z)= - 4*sin(2*z)*sum(((q)^(2*n))/(1 + 2*(q)^(2*n)* cos(2*z)+ (q)^(4*n)), n = 1..infinity) |
Divide[D[EllipticTheta[2, temp, q], {temp, 1}]/.temp-> z,EllipticTheta[2, z, q]]+ Tan[z]= - 4*Sin[2*z]*Sum[Divide[(q)^(2*n),1 + 2*(q)^(2*n)* Cos[2*z]+ (q)^(4*n)], {n, 1, Infinity}] |
Failure | Failure | Skip | Skip |
| 20.5.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -4\sin@{2z}\sum_{n=1}^{\infty}\frac{q^{2n}}{1+2q^{2n}\cos@{2z}+q^{4n}} = 4\sum_{n=1}^{\infty}(-1)^{n}\frac{q^{2n}}{1-q^{2n}}\sin@{2nz}} | - 4*sin(2*z)*sum(((q)^(2*n))/(1 + 2*(q)^(2*n)* cos(2*z)+ (q)^(4*n)), n = 1..infinity)= 4*sum((- 1)^(n)*((q)^(2*n))/(1 - (q)^(2*n))*sin(2*n*z), n = 1..infinity) |
- 4*Sin[2*z]*Sum[Divide[(q)^(2*n),1 + 2*(q)^(2*n)* Cos[2*z]+ (q)^(4*n)], {n, 1, Infinity}]= 4*Sum[(- 1)^(n)*Divide[(q)^(2*n),1 - (q)^(2*n)]*Sin[2*n*z], {n, 1, Infinity}] |
Failure | Failure | Skip | Skip |
| 20.5.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{3}'@{z}{q}}{\Jacobithetaq{3}@{z}{q}} = -4\sin@{2z}\sum_{n=1}^{\infty}\frac{q^{2n-1}}{1+2q^{2n-1}\cos@{2z}+q^{4n-2}}} | (subs( temp=z, diff( JacobiTheta3(temp, q), temp$(1) ) ))/(JacobiTheta3(z, q))= - 4*sin(2*z)*sum(((q)^(2*n - 1))/(1 + 2*(q)^(2*n - 1)* cos(2*z)+ (q)^(4*n - 2)), n = 1..infinity) |
Divide[D[EllipticTheta[3, temp, q], {temp, 1}]/.temp-> z,EllipticTheta[3, z, q]]= - 4*Sin[2*z]*Sum[Divide[(q)^(2*n - 1),1 + 2*(q)^(2*n - 1)* Cos[2*z]+ (q)^(4*n - 2)], {n, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 20.5.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle -4\sin@{2z}\sum_{n=1}^{\infty}\frac{q^{2n-1}}{1+2q^{2n-1}\cos@{2z}+q^{4n-2}} = 4\sum_{n=1}^{\infty}(-1)^{n}\frac{q^{n}}{1-q^{2n}}\sin@{2nz}} | - 4*sin(2*z)*sum(((q)^(2*n - 1))/(1 + 2*(q)^(2*n - 1)* cos(2*z)+ (q)^(4*n - 2)), n = 1..infinity)= 4*sum((- 1)^(n)*((q)^(n))/(1 - (q)^(2*n))*sin(2*n*z), n = 1..infinity) |
- 4*Sin[2*z]*Sum[Divide[(q)^(2*n - 1),1 + 2*(q)^(2*n - 1)* Cos[2*z]+ (q)^(4*n - 2)], {n, 1, Infinity}]= 4*Sum[(- 1)^(n)*Divide[(q)^(n),1 - (q)^(2*n)]*Sin[2*n*z], {n, 1, Infinity}] |
Failure | Failure | Skip | Skip |
| 20.5.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{4}'@{z}{q}}{\Jacobithetaq{4}@{z}{q}} = 4\sin@{2z}\sum_{n=1}^{\infty}\frac{q^{2n-1}}{1-2q^{2n-1}\cos@{2z}+q^{4n-2}}} | (subs( temp=z, diff( JacobiTheta4(temp, q), temp$(1) ) ))/(JacobiTheta4(z, q))= 4*sin(2*z)*sum(((q)^(2*n - 1))/(1 - 2*(q)^(2*n - 1)* cos(2*z)+ (q)^(4*n - 2)), n = 1..infinity) |
Divide[D[EllipticTheta[4, temp, q], {temp, 1}]/.temp-> z,EllipticTheta[4, z, q]]= 4*Sin[2*z]*Sum[Divide[(q)^(2*n - 1),1 - 2*(q)^(2*n - 1)* Cos[2*z]+ (q)^(4*n - 2)], {n, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 20.5.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 4\sin@{2z}\sum_{n=1}^{\infty}\frac{q^{2n-1}}{1-2q^{2n-1}\cos@{2z}+q^{4n-2}} = 4\sum_{n=1}^{\infty}\frac{q^{n}}{1-q^{2n}}\sin@{2nz}} | 4*sin(2*z)*sum(((q)^(2*n - 1))/(1 - 2*(q)^(2*n - 1)* cos(2*z)+ (q)^(4*n - 2)), n = 1..infinity)= 4*sum(((q)^(n))/(1 - (q)^(2*n))*sin(2*n*z), n = 1..infinity) |
4*Sin[2*z]*Sum[Divide[(q)^(2*n - 1),1 - 2*(q)^(2*n - 1)* Cos[2*z]+ (q)^(4*n - 2)], {n, 1, Infinity}]= 4*Sum[Divide[(q)^(n),1 - (q)^(2*n)]*Sin[2*n*z], {n, 1, Infinity}] |
Failure | Failure | Skip | Error |
| 20.5.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{2}@{z}{\tau} = \Jacobithetatau{2}@{0}{\tau}\*\lim_{N\to\infty}\prod_{n=-N}^{N}\lim_{M\to\infty}\prod_{m=1-M}^{M}\left(1+\frac{z}{(m-\tfrac{1}{2}+n\tau)\pi}\right)} | JacobiTheta2(z,exp(I*Pi*tau))= JacobiTheta2(0,exp(I*Pi*tau))* limit(product(limit(product(1 +(z)/((m -(1)/(2)+ n*tau)* Pi), m = 1 - M..M), M = infinity), n = - N..N), N = infinity) |
EllipticTheta[2, z, \[Tau]]= EllipticTheta[2, 0, \[Tau]]* Limit[Product[Limit[Product[1 +Divide[z,(m -Divide[1,2]+ n*\[Tau])* Pi], {m, 1 - M, M}], M -> Infinity], {n, - N, N}], N -> Infinity] |
Failure | Failure | Skip | Error |
| 20.5.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{3}@{z}{\tau} = \Jacobithetatau{3}@{0}{\tau}\*\lim_{N\to\infty}\prod_{n=1-N}^{N}\lim_{M\to\infty}\prod_{m=1-M}^{M}\left(1+\frac{z}{(m-\tfrac{1}{2}+(n-\tfrac{1}{2})\tau)\pi}\right)} | JacobiTheta3(z,exp(I*Pi*tau))= JacobiTheta3(0,exp(I*Pi*tau))* limit(product(limit(product(1 +(z)/((m -(1)/(2)+(n -(1)/(2))*tau)* Pi), m = 1 - M..M), M = infinity), n = 1 - N..N), N = infinity) |
EllipticTheta[3, z, \[Tau]]= EllipticTheta[3, 0, \[Tau]]* Limit[Product[Limit[Product[1 +Divide[z,(m -Divide[1,2]+(n -Divide[1,2])*\[Tau])* Pi], {m, 1 - M, M}], M -> Infinity], {n, 1 - N, N}], N -> Infinity] |
Failure | Failure | Skip | Error |
| 20.5.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{4}@{z}{\tau} = \Jacobithetatau{4}@{0}{\tau}\*\lim_{N\to\infty}\prod_{n=1-N}^{N}\lim_{M\to\infty}\prod_{m=-M}^{M}\left(1+\frac{z}{(m+(n-\tfrac{1}{2})\tau)\pi}\right)} | JacobiTheta4(z,exp(I*Pi*tau))= JacobiTheta4(0,exp(I*Pi*tau))* limit(product(limit(product(1 +(z)/((m +(n -(1)/(2))*tau)* Pi), m = - M..M), M = infinity), n = 1 - N..N), N = infinity) |
EllipticTheta[4, z, \[Tau]]= EllipticTheta[4, 0, \[Tau]]* Limit[Product[Limit[Product[1 +Divide[z,(m +(n -Divide[1,2])*\[Tau])* Pi], {m, - M, M}], M -> Infinity], {n, 1 - N, N}], N -> Infinity] |
Failure | Failure | Skip | Error |
| 20.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{1}@{\pi z}{\tau} = \pi z\Jacobithetatau{1}'@{0}{\tau}\exp@{-\sum_{j=1}^{\infty}\frac{1}{2j}\delta_{2j}(\tau)z^{2j}}} | JacobiTheta1(Pi*z,exp(I*Pi*tau))= Pi*z*subs( temp=0, diff( JacobiTheta1(temp,exp(I*Pi*tau)), temp$(1) ) )*exp(- sum((1)/(2*j)*delta[2*j]*(tau)* (z)^(2*j), j = 1..infinity)) |
EllipticTheta[1, Pi*z, \[Tau]]= Pi*z*(D[EllipticTheta[1, temp, \[Tau]], {temp, 1}]/.temp-> 0)*Exp[- Sum[Divide[1,2*j]*Subscript[\[Delta], 2*j]*(\[Tau])* (z)^(2*j), {j, 1, Infinity}]] |
Failure | Failure | Skip | Skip |
| 20.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{2}@{\pi z}{\tau} = \Jacobithetatau{2}@{0}{\tau}\exp@{-\sum_{j=1}^{\infty}\frac{1}{2j}\alpha_{2j}(\tau)z^{2j}}} | JacobiTheta2(Pi*z,exp(I*Pi*tau))= JacobiTheta2(0,exp(I*Pi*tau))*exp(- sum((1)/(2*j)*alpha[2*j]*(tau)* (z)^(2*j), j = 1..infinity)) |
EllipticTheta[2, Pi*z, \[Tau]]= EllipticTheta[2, 0, \[Tau]]*Exp[- Sum[Divide[1,2*j]*Subscript[\[Alpha], 2*j]*(\[Tau])* (z)^(2*j), {j, 1, Infinity}]] |
Failure | Failure | Skip | Skip |
| 20.6.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{3}@{\pi z}{\tau} = \Jacobithetatau{3}@{0}{\tau}\exp@{-\sum_{j=1}^{\infty}\frac{1}{2j}\beta_{2j}(\tau)z^{2j}}} | JacobiTheta3(Pi*z,exp(I*Pi*tau))= JacobiTheta3(0,exp(I*Pi*tau))*exp(- sum((1)/(2*j)*beta[2*j]*(tau)* (z)^(2*j), j = 1..infinity)) |
EllipticTheta[3, Pi*z, \[Tau]]= EllipticTheta[3, 0, \[Tau]]*Exp[- Sum[Divide[1,2*j]*Subscript[\[Beta], 2*j]*(\[Tau])* (z)^(2*j), {j, 1, Infinity}]] |
Failure | Failure | Skip | Skip |
| 20.6.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{4}@{\pi z}{\tau} = \Jacobithetatau{4}@{0}{\tau}\exp@{-\sum_{j=1}^{\infty}\frac{1}{2j}\gamma_{2j}(\tau)z^{2j}}} | JacobiTheta4(Pi*z,exp(I*Pi*tau))= JacobiTheta4(0,exp(I*Pi*tau))*exp(- sum((1)/(2*j)*gamma[2*j]*(tau)* (z)^(2*j), j = 1..infinity)) |
EllipticTheta[4, Pi*z, \[Tau]]= EllipticTheta[4, 0, \[Tau]]*Exp[- Sum[Divide[1,2*j]*Subscript[\[Gamma], 2*j]*(\[Tau])* (z)^(2*j), {j, 1, Infinity}]] |
Failure | Failure | Skip | Skip |
| 20.7.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{3}^{2}@{0}{q}\Jacobithetaq{3}^{2}@{z}{q} = \Jacobithetaq{4}^{2}@{0}{q}\Jacobithetaq{4}^{2}@{z}{q}+\Jacobithetaq{2}^{2}@{0}{q}\Jacobithetaq{2}^{2}@{z}{q}} | (JacobiTheta3(0, q))^(2)* (JacobiTheta3(z, q))^(2)= (JacobiTheta4(0, q))^(2)* (JacobiTheta4(z, q))^(2)+ (JacobiTheta2(0, q))^(2)* (JacobiTheta2(z, q))^(2) |
(EllipticTheta[3, 0, q])^(2)* (EllipticTheta[3, z, q])^(2)= (EllipticTheta[4, 0, q])^(2)* (EllipticTheta[4, z, q])^(2)+ (EllipticTheta[2, 0, q])^(2)* (EllipticTheta[2, z, q])^(2) |
Failure | Failure | Error | Successful |
| 20.7.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{3}^{2}@{0}{q}\Jacobithetaq{4}^{2}@{z}{q} = \Jacobithetaq{2}^{2}@{0}{q}\Jacobithetaq{1}^{2}@{z}{q}+\Jacobithetaq{4}^{2}@{0}{q}\Jacobithetaq{3}^{2}@{z}{q}} | (JacobiTheta3(0, q))^(2)* (JacobiTheta4(z, q))^(2)= (JacobiTheta2(0, q))^(2)* (JacobiTheta1(z, q))^(2)+ (JacobiTheta4(0, q))^(2)* (JacobiTheta3(z, q))^(2) |
(EllipticTheta[3, 0, q])^(2)* (EllipticTheta[4, z, q])^(2)= (EllipticTheta[2, 0, q])^(2)* (EllipticTheta[1, z, q])^(2)+ (EllipticTheta[4, 0, q])^(2)* (EllipticTheta[3, z, q])^(2) |
Failure | Failure | Error | Successful |
| 20.7.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{2}^{2}@{0}{q}\Jacobithetaq{4}^{2}@{z}{q} = \Jacobithetaq{3}^{2}@{0}{q}\Jacobithetaq{1}^{2}@{z}{q}+\Jacobithetaq{4}^{2}@{0}{q}\Jacobithetaq{2}^{2}@{z}{q}} | (JacobiTheta2(0, q))^(2)* (JacobiTheta4(z, q))^(2)= (JacobiTheta3(0, q))^(2)* (JacobiTheta1(z, q))^(2)+ (JacobiTheta4(0, q))^(2)* (JacobiTheta2(z, q))^(2) |
(EllipticTheta[2, 0, q])^(2)* (EllipticTheta[4, z, q])^(2)= (EllipticTheta[3, 0, q])^(2)* (EllipticTheta[1, z, q])^(2)+ (EllipticTheta[4, 0, q])^(2)* (EllipticTheta[2, z, q])^(2) |
Failure | Failure | Error | Successful |
| 20.7.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{2}^{2}@{0}{q}\Jacobithetaq{3}^{2}@{z}{q} = \Jacobithetaq{4}^{2}@{0}{q}\Jacobithetaq{1}^{2}@{z}{q}+\Jacobithetaq{3}^{2}@{0}{q}\Jacobithetaq{2}^{2}@{z}{q}} | (JacobiTheta2(0, q))^(2)* (JacobiTheta3(z, q))^(2)= (JacobiTheta4(0, q))^(2)* (JacobiTheta1(z, q))^(2)+ (JacobiTheta3(0, q))^(2)* (JacobiTheta2(z, q))^(2) |
(EllipticTheta[2, 0, q])^(2)* (EllipticTheta[3, z, q])^(2)= (EllipticTheta[4, 0, q])^(2)* (EllipticTheta[1, z, q])^(2)+ (EllipticTheta[3, 0, q])^(2)* (EllipticTheta[2, z, q])^(2) |
Failure | Failure | Error | Successful |
| 20.7.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{3}^{4}@{0}{q} = \Jacobithetaq{2}^{4}@{0}{q}+\Jacobithetaq{4}^{4}@{0}{q}} | (JacobiTheta3(0, q))^(4)= (JacobiTheta2(0, q))^(4)+ (JacobiTheta4(0, q))^(4) |
(EllipticTheta[3, 0, q])^(4)= (EllipticTheta[2, 0, q])^(4)+ (EllipticTheta[4, 0, q])^(4) |
Successful | Failure | - | Successful |
| 20.7.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{4}^{2}@{0}{q}\Jacobithetaq{1}@{w+z}{q}\Jacobithetaq{1}@{w-z}{q} = \Jacobithetaq{3}^{2}@{w}{q}\Jacobithetaq{2}^{2}@{z}{q}-\Jacobithetaq{2}^{2}@{w}{q}\Jacobithetaq{3}^{2}@{z}{q}} | (JacobiTheta4(0, q))^(2)* JacobiTheta1(w + z, q)*JacobiTheta1(w - z, q)= (JacobiTheta3(w, q))^(2)* (JacobiTheta2(z, q))^(2)- (JacobiTheta2(w, q))^(2)* (JacobiTheta3(z, q))^(2) |
(EllipticTheta[4, 0, q])^(2)* EllipticTheta[1, w + z, q]*EllipticTheta[1, w - z, q]= (EllipticTheta[3, w, q])^(2)* (EllipticTheta[2, z, q])^(2)- (EllipticTheta[2, w, q])^(2)* (EllipticTheta[3, z, q])^(2) |
Failure | Failure | Error | Successful |
| 20.7.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{4}^{2}@{0}{q}\Jacobithetaq{2}@{w+z}{q}\Jacobithetaq{2}@{w-z}{q} = \Jacobithetaq{4}^{2}@{w}{q}\Jacobithetaq{2}^{2}@{z}{q}-\Jacobithetaq{1}^{2}@{w}{q}\Jacobithetaq{3}^{2}@{z}{q}} | (JacobiTheta4(0, q))^(2)* JacobiTheta2(w + z, q)*JacobiTheta2(w - z, q)= (JacobiTheta4(w, q))^(2)* (JacobiTheta2(z, q))^(2)- (JacobiTheta1(w, q))^(2)* (JacobiTheta3(z, q))^(2) |
(EllipticTheta[4, 0, q])^(2)* EllipticTheta[2, w + z, q]*EllipticTheta[2, w - z, q]= (EllipticTheta[4, w, q])^(2)* (EllipticTheta[2, z, q])^(2)- (EllipticTheta[1, w, q])^(2)* (EllipticTheta[3, z, q])^(2) |
Failure | Failure | Error | Successful |
| 20.7.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{4}^{2}@{0}{q}\Jacobithetaq{3}@{w+z}{q}\Jacobithetaq{3}@{w-z}{q} = \Jacobithetaq{4}^{2}@{w}{q}\Jacobithetaq{3}^{2}@{z}{q}-\Jacobithetaq{1}^{2}@{w}{q}\Jacobithetaq{2}^{2}@{z}{q}} | (JacobiTheta4(0, q))^(2)* JacobiTheta3(w + z, q)*JacobiTheta3(w - z, q)= (JacobiTheta4(w, q))^(2)* (JacobiTheta3(z, q))^(2)- (JacobiTheta1(w, q))^(2)* (JacobiTheta2(z, q))^(2) |
(EllipticTheta[4, 0, q])^(2)* EllipticTheta[3, w + z, q]*EllipticTheta[3, w - z, q]= (EllipticTheta[4, w, q])^(2)* (EllipticTheta[3, z, q])^(2)- (EllipticTheta[1, w, q])^(2)* (EllipticTheta[2, z, q])^(2) |
Failure | Failure | Error | Successful |
| 20.7.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{4}^{2}@{0}{q}\Jacobithetaq{4}@{w+z}{q}\Jacobithetaq{4}@{w-z}{q} = \Jacobithetaq{3}^{2}@{w}{q}\Jacobithetaq{3}^{2}@{z}{q}-\Jacobithetaq{2}^{2}@{w}{q}\Jacobithetaq{2}^{2}@{z}{q}} | (JacobiTheta4(0, q))^(2)* JacobiTheta4(w + z, q)*JacobiTheta4(w - z, q)= (JacobiTheta3(w, q))^(2)* (JacobiTheta3(z, q))^(2)- (JacobiTheta2(w, q))^(2)* (JacobiTheta2(z, q))^(2) |
(EllipticTheta[4, 0, q])^(2)* EllipticTheta[4, w + z, q]*EllipticTheta[4, w - z, q]= (EllipticTheta[3, w, q])^(2)* (EllipticTheta[3, z, q])^(2)- (EllipticTheta[2, w, q])^(2)* (EllipticTheta[2, z, q])^(2) |
Failure | Failure | Error | Successful |
| 20.7.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{1}@{2z}{q} = 2\frac{\Jacobithetaq{1}@{z}{q}\Jacobithetaq{2}@{z}{q}\Jacobithetaq{3}@{z}{q}\Jacobithetaq{4}@{z}{q}}{\Jacobithetaq{2}@{0}{q}\Jacobithetaq{3}@{0}{q}\Jacobithetaq{4}@{0}{q}}} | JacobiTheta1(2*z, q)= 2*(JacobiTheta1(z, q)*JacobiTheta2(z, q)*JacobiTheta3(z, q)*JacobiTheta4(z, q))/(JacobiTheta2(0, q)*JacobiTheta3(0, q)*JacobiTheta4(0, q)) |
EllipticTheta[1, 2*z, q]= 2*Divide[EllipticTheta[1, z, q]*EllipticTheta[2, z, q]*EllipticTheta[3, z, q]*EllipticTheta[4, z, q],EllipticTheta[2, 0, q]*EllipticTheta[3, 0, q]*EllipticTheta[4, 0, q]] |
Failure | Failure | Error | Successful |
| 20.7.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{1}@{z}{q}\Jacobithetaq{2}@{z}{q}}{\Jacobithetaq{1}@{2z}{q^{2}}} = \frac{\Jacobithetaq{3}@{z}{q}\Jacobithetaq{4}@{z}{q}}{\Jacobithetaq{4}@{2z}{q^{2}}}} | (JacobiTheta1(z, q)*JacobiTheta2(z, q))/(JacobiTheta1(2*z, (q)^(2)))=(JacobiTheta3(z, q)*JacobiTheta4(z, q))/(JacobiTheta4(2*z, (q)^(2))) |
Divide[EllipticTheta[1, z, q]*EllipticTheta[2, z, q],EllipticTheta[1, 2*z, (q)^(2)]]=Divide[EllipticTheta[3, z, q]*EllipticTheta[4, z, q],EllipticTheta[4, 2*z, (q)^(2)]] |
Failure | Failure | Error | Successful |
| 20.7.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{3}@{z}{q}\Jacobithetaq{4}@{z}{q}}{\Jacobithetaq{4}@{2z}{q^{2}}} = \Jacobithetaq{4}@{0}{q^{2}}} | (JacobiTheta3(z, q)*JacobiTheta4(z, q))/(JacobiTheta4(2*z, (q)^(2)))= JacobiTheta4(0, (q)^(2)) |
Divide[EllipticTheta[3, z, q]*EllipticTheta[4, z, q],EllipticTheta[4, 2*z, (q)^(2)]]= EllipticTheta[4, 0, (q)^(2)] |
Failure | Failure | Error | Successful |
| 20.7.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{1}@{z}{q^{2}}\Jacobithetaq{4}@{z}{q^{2}}}{\Jacobithetaq{1}@{z}{q}} = \frac{\Jacobithetaq{2}@{z}{q^{2}}\Jacobithetaq{3}@{z}{q^{2}}}{\Jacobithetaq{2}@{z}{q}}} | (JacobiTheta1(z, (q)^(2))*JacobiTheta4(z, (q)^(2)))/(JacobiTheta1(z, q))=(JacobiTheta2(z, (q)^(2))*JacobiTheta3(z, (q)^(2)))/(JacobiTheta2(z, q)) |
Divide[EllipticTheta[1, z, (q)^(2)]*EllipticTheta[4, z, (q)^(2)],EllipticTheta[1, z, q]]=Divide[EllipticTheta[2, z, (q)^(2)]*EllipticTheta[3, z, (q)^(2)],EllipticTheta[2, z, q]] |
Failure | Failure | Error | Successful |
| 20.7.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{2}@{z}{q^{2}}\Jacobithetaq{3}@{z}{q^{2}}}{\Jacobithetaq{2}@{z}{q}} = \tfrac{1}{2}\Jacobithetaq{2}@{0}{q}} | (JacobiTheta2(z, (q)^(2))*JacobiTheta3(z, (q)^(2)))/(JacobiTheta2(z, q))=(1)/(2)*JacobiTheta2(0, q) |
Divide[EllipticTheta[2, z, (q)^(2)]*EllipticTheta[3, z, (q)^(2)],EllipticTheta[2, z, q]]=Divide[1,2]*EllipticTheta[2, 0, q] |
Failure | Failure | Error | Successful |
| 20.7.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{1}@{z}{q}\Jacobithetaq{1}@{w}{q} = \Jacobithetaq{3}@{z+w}{q^{2}}\Jacobithetaq{2}@{z-w}{q^{2}}-\Jacobithetaq{2}@{z+w}{q^{2}}\Jacobithetaq{3}@{z-w}{q^{2}}} | JacobiTheta1(z, q)*JacobiTheta1(w, q)= JacobiTheta3(z + w, (q)^(2))*JacobiTheta2(z - w, (q)^(2))- JacobiTheta2(z + w, (q)^(2))*JacobiTheta3(z - w, (q)^(2)) |
EllipticTheta[1, z, q]*EllipticTheta[1, w, q]= EllipticTheta[3, z + w, (q)^(2)]*EllipticTheta[2, z - w, (q)^(2)]- EllipticTheta[2, z + w, (q)^(2)]*EllipticTheta[3, z - w, (q)^(2)] |
Failure | Failure | Error | Successful |
| 20.7.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetaq{3}@{z}{q}\Jacobithetaq{3}@{w}{q} = \Jacobithetaq{3}@{z+w}{q^{2}}\Jacobithetaq{3}@{z-w}{q^{2}}+\Jacobithetaq{2}@{z+w}{q^{2}}\Jacobithetaq{2}@{z-w}{q^{2}}} | JacobiTheta3(z, q)*JacobiTheta3(w, q)= JacobiTheta3(z + w, (q)^(2))*JacobiTheta3(z - w, (q)^(2))+ JacobiTheta2(z + w, (q)^(2))*JacobiTheta2(z - w, (q)^(2)) |
EllipticTheta[3, z, q]*EllipticTheta[3, w, q]= EllipticTheta[3, z + w, (q)^(2)]*EllipticTheta[3, z - w, (q)^(2)]+ EllipticTheta[2, z + w, (q)^(2)]*EllipticTheta[2, z - w, (q)^(2)] |
Failure | Failure | Error | Successful |
| 20.7.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{1}@{2z}{2\tau} = A\Jacobithetatau{1}@{z}{\tau}\Jacobithetatau{2}@{z}{\tau}} | JacobiTheta1(2*z,exp(I*Pi*2*tau))= A*JacobiTheta1(z,exp(I*Pi*tau))*JacobiTheta2(z,exp(I*Pi*tau)) |
EllipticTheta[1, 2*z, 2*\[Tau]]= A*EllipticTheta[1, z, \[Tau]]*EllipticTheta[2, z, \[Tau]] |
Failure | Failure | Error | Successful |
| 20.7.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{2}@{2z}{2\tau} = A\Jacobithetatau{1}@{\tfrac{1}{4}\pi-z}{\tau}\Jacobithetatau{1}@{\tfrac{1}{4}\pi+z}{\tau}} | JacobiTheta2(2*z,exp(I*Pi*2*tau))= A*JacobiTheta1((1)/(4)*Pi - z,exp(I*Pi*tau))*JacobiTheta1((1)/(4)*Pi + z,exp(I*Pi*tau)) |
EllipticTheta[2, 2*z, 2*\[Tau]]= A*EllipticTheta[1, Divide[1,4]*Pi - z, \[Tau]]*EllipticTheta[1, Divide[1,4]*Pi + z, \[Tau]] |
Error | Failure | - | Successful |
| 20.7.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{3}@{2z}{2\tau} = A\Jacobithetatau{3}@{\tfrac{1}{4}\pi-z}{\tau}\Jacobithetatau{3}@{\tfrac{1}{4}\pi+z}{\tau}} | JacobiTheta3(2*z,exp(I*Pi*2*tau))= A*JacobiTheta3((1)/(4)*Pi - z,exp(I*Pi*tau))*JacobiTheta3((1)/(4)*Pi + z,exp(I*Pi*tau)) |
EllipticTheta[3, 2*z, 2*\[Tau]]= A*EllipticTheta[3, Divide[1,4]*Pi - z, \[Tau]]*EllipticTheta[3, Divide[1,4]*Pi + z, \[Tau]] |
Error | Failure | - | Successful |
| 20.7.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{4}@{2z}{2\tau} = A\Jacobithetatau{3}@{z}{\tau}\Jacobithetatau{4}@{z}{\tau}} | JacobiTheta4(2*z,exp(I*Pi*2*tau))= A*JacobiTheta3(z,exp(I*Pi*tau))*JacobiTheta4(z,exp(I*Pi*tau)) |
EllipticTheta[4, 2*z, 2*\[Tau]]= A*EllipticTheta[3, z, \[Tau]]*EllipticTheta[4, z, \[Tau]] |
Failure | Failure | Error | Successful |
| 20.7.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{1}@{4z}{4\tau} = B\Jacobithetatau{1}@{z}{\tau}\Jacobithetatau{1}@{\tfrac{1}{4}\pi-z}{\tau}\*\Jacobithetatau{1}@{\tfrac{1}{4}\pi+z}{\tau}\Jacobithetatau{2}@{z}{\tau}} | JacobiTheta1(4*z,exp(I*Pi*4*tau))= B*JacobiTheta1(z,exp(I*Pi*tau))*JacobiTheta1((1)/(4)*Pi - z,exp(I*Pi*tau))* JacobiTheta1((1)/(4)*Pi + z,exp(I*Pi*tau))*JacobiTheta2(z,exp(I*Pi*tau)) |
EllipticTheta[1, 4*z, 4*\[Tau]]= B*EllipticTheta[1, z, \[Tau]]*EllipticTheta[1, Divide[1,4]*Pi - z, \[Tau]]* EllipticTheta[1, Divide[1,4]*Pi + z, \[Tau]]*EllipticTheta[2, z, \[Tau]] |
Error | Failure | - | Successful |
| 20.7.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{2}@{4z}{4\tau} = B\Jacobithetatau{2}@{\tfrac{1}{8}\pi-z}{\tau}\Jacobithetatau{2}@{\tfrac{1}{8}\pi+z}{\tau}\*\Jacobithetatau{2}@{\tfrac{3}{8}\pi-z}{\tau}\Jacobithetatau{2}@{\tfrac{3}{8}\pi+z}{\tau}} | JacobiTheta2(4*z,exp(I*Pi*4*tau))= B*JacobiTheta2((1)/(8)*Pi - z,exp(I*Pi*tau))*JacobiTheta2((1)/(8)*Pi + z,exp(I*Pi*tau))* JacobiTheta2((3)/(8)*Pi - z,exp(I*Pi*tau))*JacobiTheta2((3)/(8)*Pi + z,exp(I*Pi*tau)) |
EllipticTheta[2, 4*z, 4*\[Tau]]= B*EllipticTheta[2, Divide[1,8]*Pi - z, \[Tau]]*EllipticTheta[2, Divide[1,8]*Pi + z, \[Tau]]* EllipticTheta[2, Divide[3,8]*Pi - z, \[Tau]]*EllipticTheta[2, Divide[3,8]*Pi + z, \[Tau]] |
Error | Failure | - | Successful |
| 20.7.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{3}@{4z}{4\tau} = B\Jacobithetatau{3}@{\tfrac{1}{8}\pi-z}{\tau}\Jacobithetatau{3}@{\tfrac{1}{8}\pi+z}{\tau}\*\Jacobithetatau{3}@{\tfrac{3}{8}\pi-z}{\tau}\Jacobithetatau{3}@{\tfrac{3}{8}\pi+z}{\tau}} | JacobiTheta3(4*z,exp(I*Pi*4*tau))= B*JacobiTheta3((1)/(8)*Pi - z,exp(I*Pi*tau))*JacobiTheta3((1)/(8)*Pi + z,exp(I*Pi*tau))* JacobiTheta3((3)/(8)*Pi - z,exp(I*Pi*tau))*JacobiTheta3((3)/(8)*Pi + z,exp(I*Pi*tau)) |
EllipticTheta[3, 4*z, 4*\[Tau]]= B*EllipticTheta[3, Divide[1,8]*Pi - z, \[Tau]]*EllipticTheta[3, Divide[1,8]*Pi + z, \[Tau]]* EllipticTheta[3, Divide[3,8]*Pi - z, \[Tau]]*EllipticTheta[3, Divide[3,8]*Pi + z, \[Tau]] |
Error | Failure | - | Successful |
| 20.7.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{4}@{4z}{4\tau} = B\Jacobithetatau{4}@{z}{\tau}\Jacobithetatau{4}@{\tfrac{1}{4}\pi-z}{\tau}\*\Jacobithetatau{4}@{\tfrac{1}{4}\pi+z}{\tau}\Jacobithetatau{3}@{z}{\tau}} | JacobiTheta4(4*z,exp(I*Pi*4*tau))= B*JacobiTheta4(z,exp(I*Pi*tau))*JacobiTheta4((1)/(4)*Pi - z,exp(I*Pi*tau))* JacobiTheta4((1)/(4)*Pi + z,exp(I*Pi*tau))*JacobiTheta3(z,exp(I*Pi*tau)) |
EllipticTheta[4, 4*z, 4*\[Tau]]= B*EllipticTheta[4, z, \[Tau]]*EllipticTheta[4, Divide[1,4]*Pi - z, \[Tau]]* EllipticTheta[4, Divide[1,4]*Pi + z, \[Tau]]*EllipticTheta[3, z, \[Tau]] |
Error | Failure | - | Successful |
| 20.7.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv{}{z}\left(\frac{\Jacobithetatau{2}@{z}{\tau}}{\Jacobithetatau{4}@{z}{\tau}}\right) = -\frac{\Jacobithetatau{3}^{2}@{0}{\tau}\Jacobithetatau{1}@{z}{\tau}\Jacobithetatau{3}@{z}{\tau}}{\Jacobithetatau{4}^{2}@{z}{\tau}}} | diff((JacobiTheta2(z,exp(I*Pi*tau)))/(JacobiTheta4(z,exp(I*Pi*tau))), z)= -((JacobiTheta3(0,exp(I*Pi*tau)))^(2)* JacobiTheta1(z,exp(I*Pi*tau))*JacobiTheta3(z,exp(I*Pi*tau)))/((JacobiTheta4(z,exp(I*Pi*tau)))^(2)) |
D[Divide[EllipticTheta[2, z, \[Tau]],EllipticTheta[4, z, \[Tau]]], z]= -Divide[(EllipticTheta[3, 0, \[Tau]])^(2)* EllipticTheta[1, z, \[Tau]]*EllipticTheta[3, z, \[Tau]],(EllipticTheta[4, z, \[Tau]])^(2)] |
Failure | Failure | Error | Successful |
| 20.7.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{1}@{z}{\tau+1} = e^{i\pi/4}\Jacobithetatau{1}@{z}{\tau}} | JacobiTheta1(z,exp(I*Pi*tau + 1))= exp(I*Pi/ 4)*JacobiTheta1(z,exp(I*Pi*tau)) |
EllipticTheta[1, z, \[Tau]+ 1]= Exp[I*Pi/ 4]*EllipticTheta[1, z, \[Tau]] |
Failure | Failure | Error | Successful |
| 20.7.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{2}@{z}{\tau+1} = e^{i\pi/4}\Jacobithetatau{2}@{z}{\tau}} | JacobiTheta2(z,exp(I*Pi*tau + 1))= exp(I*Pi/ 4)*JacobiTheta2(z,exp(I*Pi*tau)) |
EllipticTheta[2, z, \[Tau]+ 1]= Exp[I*Pi/ 4]*EllipticTheta[2, z, \[Tau]] |
Failure | Failure | Error | Successful |
| 20.7.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{3}@{z}{\tau+1} = \Jacobithetatau{4}@{z}{\tau}} | JacobiTheta3(z,exp(I*Pi*tau + 1))= JacobiTheta4(z,exp(I*Pi*tau)) |
EllipticTheta[3, z, \[Tau]+ 1]= EllipticTheta[4, z, \[Tau]] |
Failure | Failure | Error | Successful |
| 20.7.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Jacobithetatau{4}@{z}{\tau+1} = \Jacobithetatau{3}@{z}{\tau}} | JacobiTheta4(z,exp(I*Pi*tau + 1))= JacobiTheta3(z,exp(I*Pi*tau)) |
EllipticTheta[4, z, \[Tau]+ 1]= EllipticTheta[3, z, \[Tau]] |
Failure | Failure | Error | Successful |
| 20.7.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{1}@{z}{q^{2}}\Jacobithetaq{3}@{z}{q^{2}}}{\Jacobithetaq{1}@{z}{iq}} = \frac{\Jacobithetaq{2}@{z}{q^{2}}\Jacobithetaq{4}@{z}{q^{2}}}{\Jacobithetaq{2}@{z}{iq}}} | (JacobiTheta1(z, (q)^(2))*JacobiTheta3(z, (q)^(2)))/(JacobiTheta1(z, I*q))=(JacobiTheta2(z, (q)^(2))*JacobiTheta4(z, (q)^(2)))/(JacobiTheta2(z, I*q)) |
Divide[EllipticTheta[1, z, (q)^(2)]*EllipticTheta[3, z, (q)^(2)],EllipticTheta[1, z, I*q]]=Divide[EllipticTheta[2, z, (q)^(2)]*EllipticTheta[4, z, (q)^(2)],EllipticTheta[2, z, I*q]] |
Failure | Failure | Error | Successful |
| 20.7.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{2}@{z}{q^{2}}\Jacobithetaq{4}@{z}{q^{2}}}{\Jacobithetaq{2}@{z}{iq}} = i^{-1/4}\sqrt{\frac{\Jacobithetaq{2}@{0}{q^{2}}\Jacobithetaq{4}@{0}{q^{2}}}{2}}} | (JacobiTheta2(z, (q)^(2))*JacobiTheta4(z, (q)^(2)))/(JacobiTheta2(z, I*q))= (I)^(- 1/ 4)*sqrt((JacobiTheta2(0, (q)^(2))*JacobiTheta4(0, (q)^(2)))/(2)) |
Divide[EllipticTheta[2, z, (q)^(2)]*EllipticTheta[4, z, (q)^(2)],EllipticTheta[2, z, I*q]]= (I)^(- 1/ 4)*Sqrt[Divide[EllipticTheta[2, 0, (q)^(2)]*EllipticTheta[4, 0, (q)^(2)],2]] |
Failure | Failure | Error | Successful |
| 20.8.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\Jacobithetaq{2}@{0}{q}\Jacobithetaq{3}@{z}{q}\Jacobithetaq{4}@{z}{q}}{\Jacobithetaq{2}@{z}{q}} = 2\sum_{n=-\infty}^{\infty}\frac{(-1)^{n}q^{n^{2}}e^{i2nz}}{q^{-n}e^{-iz}+q^{n}e^{iz}}} | (JacobiTheta2(0, q)*JacobiTheta3(z, q)*JacobiTheta4(z, q))/(JacobiTheta2(z, q))= 2*sum(((- 1)^(n)* (q)^((n)^(2))* exp(I*2*n*z))/((q)^(- n)* exp(- I*z)+ (q)^(n)* exp(I*z)), n = - infinity..infinity) |
Divide[EllipticTheta[2, 0, q]*EllipticTheta[3, z, q]*EllipticTheta[4, z, q],EllipticTheta[2, z, q]]= 2*Sum[Divide[(- 1)^(n)* (q)^((n)^(2))* Exp[I*2*n*z],(q)^(- n)* Exp[- I*z]+ (q)^(n)* Exp[I*z]], {n, - Infinity, Infinity}] |
Failure | Failure | Skip | Error |
| 20.9#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk@{k} = \tfrac{1}{2}\pi\Jacobithetatau{3}^{2}@{0}{\tau}} | EllipticK(k)=(1)/(2)*Pi*(JacobiTheta3(0,exp(I*Pi*tau)))^(2) |
EllipticK[(k)^2]=Divide[1,2]*Pi*(EllipticTheta[3, 0, \[Tau]])^(2) |
Failure | Failure | Error | Fail
DirectedInfinity[] <- {Rule[k, 1], Rule[τ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}DirectedInfinity[] <- {Rule[k, 1], Rule[τ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}DirectedInfinity[] <- {Rule[k, 1], Rule[τ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}DirectedInfinity[] <- {Rule[k, 1], Rule[τ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 20.9#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \compellintKk'@{k} = -i\tau\compellintKk@{k}} | subs( temp=k, diff( EllipticK(temp), temp$(1) ) )= - I*tau*EllipticK(k) |
(D[EllipticK[(temp)^2], {temp, 1}]/.temp-> k)= - I*\[Tau]*EllipticK[(k)^2] |
Failure | Failure | Error | Fail
Complex[-0.1562727389735284, 3.03204555200124] <- {Rule[k, 2], Rule[τ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[0.23878593395814385, 2.131309480129808] <- {Rule[k, 3], Rule[τ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}Complex[2.227738275577703, -0.017728124162552983] <- {Rule[k, 2], Rule[τ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[1.7636727720400398, -0.25270153442142274] <- {Rule[k, 3], Rule[τ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 20.9.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{\frac{\Jacobithetaq{2}^{2}@{z}{q}}{\Jacobithetaq{2}^{2}@{0}{q}}}{\frac{\Jacobithetaq{3}^{2}@{z}{q}}{\Jacobithetaq{3}^{2}@{0}{q}}}{\frac{\Jacobithetaq{4}^{2}@{z}{q}}{\Jacobithetaq{4}^{2}@{0}{q}}} = \frac{\Jacobithetaq{1}'@{0}{q}}{\Jacobithetaq{1}@{z}{q}}z} | 0.5*int(1/(sqrt(t+((JacobiTheta2(z, q))^(2))/((JacobiTheta2(0, q))^(2)))*sqrt(t+((JacobiTheta3(z, q))^(2))/((JacobiTheta3(0, q))^(2)))*sqrt(t+((JacobiTheta4(z, q))^(2))/((JacobiTheta4(0, q))^(2)))), t = 0..infinity)=(subs( temp=0, diff( JacobiTheta1(temp, q), temp$(1) ) ))/(JacobiTheta1(z, q))*z |
Error |
Error | Error | - | - |
| 20.9.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \CarlsonsymellintRF@{0}{\Jacobithetaq{3}^{4}@{0}{q}}{\Jacobithetaq{4}^{4}@{0}{q}} = \tfrac{1}{2}\pi} | 0.5*int(1/(sqrt(t+0)*sqrt(t+(JacobiTheta3(0, q))^(4))*sqrt(t+(JacobiTheta4(0, q))^(4))), t = 0..infinity)=(1)/(2)*Pi |
Error |
Error | Error | - | - |
| 20.10.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}x^{s-1}\Jacobithetatau{2}@{0}{ix^{2}}\diff{x} = 2^{s}(1-2^{-s})\pi^{-s/2}\EulerGamma@{\tfrac{1}{2}s}\Riemannzeta@{s}} | int((x)^(s - 1)* JacobiTheta2(0,exp(I*Pi*I*(x)^(2))), x = 0..infinity)= (2)^(s)*(1 - (2)^(- s))* (Pi)^(- s/ 2)* GAMMA((1)/(2)*s)*Zeta(s) |
Integrate[(x)^(s - 1)* EllipticTheta[2, 0, I*(x)^(2)], {x, 0, Infinity}]= (2)^(s)*(1 - (2)^(- s))* (Pi)^(- s/ 2)* Gamma[Divide[1,2]*s]*Zeta[s] |
Failure | Failure | Skip | Error |
| 20.10.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}x^{s-1}(\Jacobithetatau{3}@{0}{ix^{2}}-1)\diff{x} = \pi^{-s/2}\EulerGamma@{\tfrac{1}{2}s}\Riemannzeta@{s}} | int((x)^(s - 1)*(JacobiTheta3(0,exp(I*Pi*I*(x)^(2)))- 1), x = 0..infinity)= (Pi)^(- s/ 2)* GAMMA((1)/(2)*s)*Zeta(s) |
Integrate[(x)^(s - 1)*(EllipticTheta[3, 0, I*(x)^(2)]- 1), {x, 0, Infinity}]= (Pi)^(- s/ 2)* Gamma[Divide[1,2]*s]*Zeta[s] |
Failure | Failure | Skip | Error |
| 20.10.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}x^{s-1}(1-\Jacobithetatau{4}@{0}{ix^{2}})\diff{x} = (1-2^{1-s})\pi^{-s/2}\EulerGamma@{\tfrac{1}{2}s}\Riemannzeta@{s}} | int((x)^(s - 1)*(1 - JacobiTheta4(0,exp(I*Pi*I*(x)^(2)))), x = 0..infinity)=(1 - (2)^(1 - s))* (Pi)^(- s/ 2)* GAMMA((1)/(2)*s)*Zeta(s) |
Integrate[(x)^(s - 1)*(1 - EllipticTheta[4, 0, I*(x)^(2)]), {x, 0, Infinity}]=(1 - (2)^(1 - s))* (Pi)^(- s/ 2)* Gamma[Divide[1,2]*s]*Zeta[s] |
Failure | Failure | Skip | Error |
| 20.10.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-st}\Jacobithetatau{1}@{\frac{\beta\pi}{2\ell}}{\frac{i\pi t}{\ell^{2}}}\diff{t} = \int_{0}^{\infty}e^{-st}\Jacobithetatau{2}@{\frac{(1+\beta)\pi}{2\ell}}{\frac{i\pi t}{\ell^{2}}}\diff{t}} | - stint(exp(1)*JacobiTheta1((beta*Pi)/(2*ell),exp(I*Pi*(I*Pi*t)/((ell)^(2)))), t = 0..infinity)= - stint(exp(1)*JacobiTheta2(((1 + beta)* Pi)/(2*ell),exp(I*Pi*(I*Pi*t)/((ell)^(2)))), t = 0..infinity) |
- stIntegrate[E*EllipticTheta[1, Divide[\[Beta]*Pi,2*\[ScriptL]], Divide[I*Pi*t,(\[ScriptL])^(2)]], {t, 0, Infinity}]= - stIntegrate[E*EllipticTheta[2, Divide[(1 + \[Beta])* Pi,2*\[ScriptL]], Divide[I*Pi*t,(\[ScriptL])^(2)]], {t, 0, Infinity}] |
Failure | Failure | Skip | Fail
Complex[0.0, -2.8284271247461903] <- {Rule[stIntegrate[Times[E, EllipticTheta[1, Times[Rational[1, 2], Pi, Power[ℓ, -1], β], Times[Complex[0, 1], Pi, t, Power[ℓ, -2]]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[stIntegrate[Times[E, EllipticTheta[2, Times[Rational[1, 2], Pi, Power[ℓ, -1], Plus[1, β]], Times[Complex[0, 1], Pi, t, Power[ℓ, -2]]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[stIntegrate[Times[E, EllipticTheta[1, Times[Rational[1, 2], Pi, Power[ℓ, -1], β], Times[Complex[0, 1], Pi, t, Power[ℓ, -2]]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[stIntegrate[Times[E, EllipticTheta[2, Times[Rational[1, 2], Pi, Power[ℓ, -1], Plus[1, β]], Times[Complex[0, 1], Pi, t, Power[ℓ, -2]]]], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-2.8284271247461903 <- {Rule[stIntegrate[Times[E, EllipticTheta[1, Times[Rational[1, 2], Pi, Power[ℓ, -1], β], Times[Complex[0, 1], Pi, t, Power[ℓ, -2]]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[stIntegrate[Times[E, EllipticTheta[2, Times[Rational[1, 2], Pi, Power[ℓ, -1], Plus[1, β]], Times[Complex[0, 1], Pi, t, Power[ℓ, -2]]]], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, 2.8284271247461903] <- {Rule[stIntegrate[Times[E, EllipticTheta[1, Times[Rational[1, 2], Pi, Power[ℓ, -1], β], Times[Complex[0, 1], Pi, t, Power[ℓ, -2]]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[stIntegrate[Times[E, EllipticTheta[2, Times[Rational[1, 2], Pi, Power[ℓ, -1], Plus[1, β]], Times[Complex[0, 1], Pi, t, Power[ℓ, -2]]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 20.10.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-st}\Jacobithetatau{2}@{\frac{(1+\beta)\pi}{2\ell}}{\frac{i\pi t}{\ell^{2}}}\diff{t} = -\frac{\ell}{\sqrt{s}}\sinh@{\beta\sqrt{s}}\sech@{\ell\sqrt{s}}} | - stint(exp(1)*JacobiTheta2(((1 + beta)* Pi)/(2*ell),exp(I*Pi*(I*Pi*t)/((ell)^(2)))), t = 0..infinity)= -(ell)/(sqrt(s))*sinh(beta*sqrt(s))*sech(ell*sqrt(s)) |
- stIntegrate[E*EllipticTheta[2, Divide[(1 + \[Beta])* Pi,2*\[ScriptL]], Divide[I*Pi*t,(\[ScriptL])^(2)]], {t, 0, Infinity}]= -Divide[\[ScriptL],Sqrt[s]]*Sinh[\[Beta]*Sqrt[s]]*Sech[\[ScriptL]*Sqrt[s]] |
Failure | Failure | Skip | Successful |
| 20.10.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-st}\Jacobithetatau{3}@{\frac{(1+\beta)\pi}{2\ell}}{\frac{i\pi t}{\ell^{2}}}\diff{t} = \int_{0}^{\infty}e^{-st}\Jacobithetatau{4}@{\frac{\beta\pi}{2\ell}}{\frac{i\pi t}{\ell^{2}}}\diff{t}} | - stint(exp(1)*JacobiTheta3(((1 + beta)* Pi)/(2*ell),exp(I*Pi*(I*Pi*t)/((ell)^(2)))), t = 0..infinity)= - stint(exp(1)*JacobiTheta4((beta*Pi)/(2*ell),exp(I*Pi*(I*Pi*t)/((ell)^(2)))), t = 0..infinity) |
- stIntegrate[E*EllipticTheta[3, Divide[(1 + \[Beta])* Pi,2*\[ScriptL]], Divide[I*Pi*t,(\[ScriptL])^(2)]], {t, 0, Infinity}]= - stIntegrate[E*EllipticTheta[4, Divide[\[Beta]*Pi,2*\[ScriptL]], Divide[I*Pi*t,(\[ScriptL])^(2)]], {t, 0, Infinity}] |
Failure | Failure | Skip | Fail
Complex[0.0, -2.8284271247461903] <- {Rule[stIntegrate[Times[E, EllipticTheta[3, Times[Rational[1, 2], Pi, Power[ℓ, -1], Plus[1, β]], Times[Complex[0, 1], Pi, t, Power[ℓ, -2]]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[stIntegrate[Times[E, EllipticTheta[4, Times[Rational[1, 2], Pi, Power[ℓ, -1], β], Times[Complex[0, 1], Pi, t, Power[ℓ, -2]]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}Complex[-2.8284271247461903, -2.8284271247461903] <- {Rule[stIntegrate[Times[E, EllipticTheta[3, Times[Rational[1, 2], Pi, Power[ℓ, -1], Plus[1, β]], Times[Complex[0, 1], Pi, t, Power[ℓ, -2]]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[stIntegrate[Times[E, EllipticTheta[4, Times[Rational[1, 2], Pi, Power[ℓ, -1], β], Times[Complex[0, 1], Pi, t, Power[ℓ, -2]]]], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}-2.8284271247461903 <- {Rule[stIntegrate[Times[E, EllipticTheta[3, Times[Rational[1, 2], Pi, Power[ℓ, -1], Plus[1, β]], Times[Complex[0, 1], Pi, t, Power[ℓ, -2]]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]], Rule[stIntegrate[Times[E, EllipticTheta[4, Times[Rational[1, 2], Pi, Power[ℓ, -1], β], Times[Complex[0, 1], Pi, t, Power[ℓ, -2]]]], {t, 0, DirectedInfinity[1]}], Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]}Complex[0.0, 2.8284271247461903] <- {Rule[stIntegrate[Times[E, EllipticTheta[3, Times[Rational[1, 2], Pi, Power[ℓ, -1], Plus[1, β]], Times[Complex[0, 1], Pi, t, Power[ℓ, -2]]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, -1], Power[2, Rational[1, 2]]]], Rule[stIntegrate[Times[E, EllipticTheta[4, Times[Rational[1, 2], Pi, Power[ℓ, -1], β], Times[Complex[0, 1], Pi, t, Power[ℓ, -2]]]], {t, 0, DirectedInfinity[1]}], Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}... skip entries to safe data |
| 20.10.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}e^{-st}\Jacobithetatau{4}@{\frac{\beta\pi}{2\ell}}{\frac{i\pi t}{\ell^{2}}}\diff{t} = \frac{\ell}{\sqrt{s}}\cosh@{\beta\sqrt{s}}\csch@{\ell\sqrt{s}}} | - stint(exp(1)*JacobiTheta4((beta*Pi)/(2*ell),exp(I*Pi*(I*Pi*t)/((ell)^(2)))), t = 0..infinity)=(ell)/(sqrt(s))*cosh(beta*sqrt(s))*csch(ell*sqrt(s)) |
- stIntegrate[E*EllipticTheta[4, Divide[\[Beta]*Pi,2*\[ScriptL]], Divide[I*Pi*t,(\[ScriptL])^(2)]], {t, 0, Infinity}]=Divide[\[ScriptL],Sqrt[s]]*Cosh[\[Beta]*Sqrt[s]]*Csch[\[ScriptL]*Sqrt[s]] |
Failure | Failure | Skip | Successful |
| 20.11.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \genhyperF{2}{1}@{\tfrac{1}{2},\tfrac{1}{2}}{1}{k^{2}} = \Jacobithetatau{3}^{2}@{0}{\tau}} | hypergeom([(1)/(2),(1)/(2)], [1], (k)^(2))= (JacobiTheta3(0,exp(I*Pi*tau)))^(2) |
HypergeometricPFQ[{Divide[1,2],Divide[1,2]}, {1}, (k)^(2)]= (EllipticTheta[3, 0, \[Tau]])^(2) |
Failure | Failure | Error | Fail
DirectedInfinity[] <- {Rule[k, 1], Rule[τ, Times[Complex[1, 1], Power[2, Rational[1, 2]]]]}DirectedInfinity[] <- {Rule[k, 1], Rule[τ, Times[Complex[1, -1], Power[2, Rational[1, 2]]]]}DirectedInfinity[] <- {Rule[k, 1], Rule[τ, Times[Complex[-1, -1], Power[2, Rational[1, 2]]]]}DirectedInfinity[] <- {Rule[k, 1], Rule[τ, Times[Complex[-1, 1], Power[2, Rational[1, 2]]]]} |
| 20.13.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \ipderiv{\theta}{t} = \alpha\ipderiv[2]{\theta}{z}} | diff(theta, t)= alpha*diff(theta, [z$(2)]) |
D[\[Theta], t]= \[Alpha]*D[\[Theta], {z, 2}] |
Successful | Successful | - | - |