Weierstrass Elliptic and Modular Functions - 23.10 Addition Theorems and Other Identities
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
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| 23.10.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle A_{n} = \left(\frac{\pi^{2}G^{2}}{\omega_{1}}\right)^{n^{2}-1}\frac{q^{n(n-1)/2}}{i^{n-1}}\exp@{-\frac{(n-1)\eta_{1}}{3\omega_{1}}\left((2n-1)(\omega_{1}^{2}+\omega_{3}^{2})+3(n-1)\omega_{1}\omega_{3}\right)}}
A_{n} = \left(\frac{\pi^{2}G^{2}}{\omega_{1}}\right)^{n^{2}-1}\frac{q^{n(n-1)/2}}{i^{n-1}}\exp@{-\frac{(n-1)\eta_{1}}{3\omega_{1}}\left((2n-1)(\omega_{1}^{2}+\omega_{3}^{2})+3(n-1)\omega_{1}\omega_{3}\right)} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | A[n] = (((Pi)^(2)* (G)^(2))/(omega[1]))^((n)^(2)- 1)*((q)^(n*(n - 1)/2))/((I)^(n - 1))*exp(-((n - 1)*eta[1])/(3*omega[1])*((2*n - 1)*((omega[1])^(2)+ (omega[3])^(2))+ 3*(n - 1)*omega[1]*omega[3]))
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Subscript[A, n] == (Divide[(Pi)^(2)* (G)^(2),Subscript[\[Omega], 1]])^((n)^(2)- 1)*Divide[(q)^(n*(n - 1)/2),(I)^(n - 1)]*Exp[-Divide[(n - 1)*Subscript[\[Eta], 1],3*Subscript[\[Omega], 1]]*((2*n - 1)*((Subscript[\[Omega], 1])^(2)+ (Subscript[\[Omega], 3])^(2))+ 3*(n - 1)*Subscript[\[Omega], 1]*Subscript[\[Omega], 3])]
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Failure | Failure | Failed [300 / 300] Result: -.1339745960+.5000000000*I
Test Values: {G = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, A[n] = 1/2*3^(1/2)+1/2*I, eta[1] = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I, n = 1}
Result: 1.057001493+.6153915143*I
Test Values: {G = 1/2*3^(1/2)+1/2*I, eta = 1/2*3^(1/2)+1/2*I, omega = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, A[n] = 1/2*3^(1/2)+1/2*I, eta[1] = 1/2*3^(1/2)+1/2*I, omega[1] = 1/2*3^(1/2)+1/2*I, omega[3] = 1/2*3^(1/2)+1/2*I, n = 2}
... skip entries to safe data |
Skipped - Because timed out |
| 23.10#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q = e^{\pi i\omega_{3}/\omega_{1}}}
q = e^{\pi i\omega_{3}/\omega_{1}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | q = exp(Pi*I*omega[3]/omega[1]) |
q == Exp[Pi*I*Subscript[\[Omega], 3]/Subscript[\[Omega], 1]] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 23.10#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle G = \prod_{n=1}^{\infty}(1-q^{2n})}
G = \prod_{n=1}^{\infty}(1-q^{2n}) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | G = product(1 - (q)^(2*n), n = 1..infinity) |
G == Product[1 - (q)^(2*n), {n, 1, Infinity}, GenerateConditions->None] |
Skipped - no semantic math | Skipped - no semantic math | - | - |