q -Hypergeometric and Related Functions - 17.12 Bailey Pairs

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DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
17.12.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\alpha_{n}\gamma_{n} = \sum_{n=0}^{\infty}\beta_{n}\delta_{n}}
\sum_{n=0}^{\infty}\alpha_{n}\gamma_{n} = \sum_{n=0}^{\infty}\beta_{n}\delta_{n}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sum(alpha[n]*gamma[n], n = 0..infinity) = sum(beta[n]*delta[n], n = 0..infinity)
 
Sum[Subscript[\[Alpha], n]*Subscript[\[Gamma], n], {n, 0, Infinity}, GenerateConditions->None] == Sum[Subscript[\[Beta], n]*Subscript[\[Delta], n], {n, 0, Infinity}, GenerateConditions->None]
 Skipped - no semantic math Skipped - no semantic math - -
17.12#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{n} = \sum_{j=0}^{n}\alpha_{j}u_{n-j}v_{n+j}}
\beta_{n} = \sum_{j=0}^{n}\alpha_{j}u_{n-j}v_{n+j}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
beta[n] = sum(alpha[j]*u[n - j]*v[n + j], j = 0..n)
 
Subscript[\[Beta], n] == Sum[Subscript[\[Alpha], j]*Subscript[u, n - j]*Subscript[v, n + j], {j, 0, n}, GenerateConditions->None]
 Skipped - no semantic math Skipped - no semantic math - -
17.12#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \gamma_{n} = \sum_{j=n}^{\infty}\delta_{j}u_{j-n}v_{j+n}}
\gamma_{n} = \sum_{j=n}^{\infty}\delta_{j}u_{j-n}v_{j+n}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
gamma[n] = sum(delta[j]*u[j - n]*v[j + n], j = n..infinity)
 
Subscript[\[Gamma], n] == Sum[Subscript[\[Delta], j]*Subscript[u, j - n]*Subscript[v, j + n], {j, n, Infinity}, GenerateConditions->None]
 Skipped - no semantic math Skipped - no semantic math - -
17.12.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{n} = \sum_{j=0}^{n}\frac{\alpha_{j}}{\qPochhammer{q}{q}{n-j}\qPochhammer{aq}{q}{n+j}}}
\beta_{n} = \sum_{j=0}^{n}\frac{\alpha_{j}}{\qPochhammer{q}{q}{n-j}\qPochhammer{aq}{q}{n+j}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
beta[n] = sum((alpha[j])/(QPochhammer(q, q, n - j)*QPochhammer(a*q, q, n + j)), j = 0..n)

Subscript[\[Beta], n] == Sum[Divide[Subscript[\[Alpha], j],QPochhammer[q, q, n - j]*QPochhammer[a*q, q, n + j]], {j, 0, n}, GenerateConditions->None]
Failure Aborted Error
Failed [300 / 300]
Result: Complex[0.6508376433032488, -0.21856268949920582]
Test Values: {Rule[a, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[Subscript[α, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[β, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[0.8660402331469415, 0.20457300495175623]
Test Values: {Rule[a, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[Subscript[α, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[β, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
17.12.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}q^{n^{2}}a^{n}\beta_{n} = \frac{1}{\qPochhammer{aq}{q}{\infty}}\sum_{n=0}^{\infty}q^{n^{2}}a^{n}\alpha_{n}}
\sum_{n=0}^{\infty}q^{n^{2}}a^{n}\beta_{n} = \frac{1}{\qPochhammer{aq}{q}{\infty}}\sum_{n=0}^{\infty}q^{n^{2}}a^{n}\alpha_{n}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sum((q)^((n)^(2))* (a)^(n)* beta[n], n = 0..infinity) = (1)/(QPochhammer(a*q, q, infinity))*sum((q)^((n)^(2))* (a)^(n)* alpha[n], n = 0..infinity)

Sum[(q)^((n)^(2))* (a)^(n)* Subscript[\[Beta], n], {n, 0, Infinity}, GenerateConditions->None] == Divide[1,QPochhammer[a*q, q, Infinity]]*Sum[(q)^((n)^(2))* (a)^(n)* Subscript[\[Alpha], n], {n, 0, Infinity}, GenerateConditions->None]
Failure Aborted Skipped - Because timed out Skipped - Because timed out
17.12#Ex5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \alpha_{n} = \frac{\qPochhammer{a}{q}{n}(1-aq^{2n})(-1)^{n}q^{n(3n-1)/2}a^{n}}{\qPochhammer{q}{q}{n}(1-a)}}
\alpha_{n} = \frac{\qPochhammer{a}{q}{n}(1-aq^{2n})(-1)^{n}q^{n(3n-1)/2}a^{n}}{\qPochhammer{q}{q}{n}(1-a)}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
alpha[n] = (QPochhammer(a, q, n)*(1 - a*(q)^(2*n))*(- 1)^(n)* (q)^(n*(3*n - 1)/2)* (a)^(n))/(QPochhammer(q, q, n)*(1 - a))

Subscript[\[Alpha], n] == Divide[QPochhammer[a, q, n]*(1 - a*(q)^(2*n))*(- 1)^(n)* (q)^(n*(3*n - 1)/2)* (a)^(n),QPochhammer[q, q, n]*(1 - a)]
Error Failure -
Failed [300 / 300]
Result: Complex[5.814582562299427, -3.4240381056766607]
Test Values: {Rule[a, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[α, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[-12.010896071760529, -4.7481964481437355]
Test Values: {Rule[a, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[α, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
17.12#Ex6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \beta_{n} = \frac{1}{\qPochhammer{q}{q}{n}}}
\beta_{n} = \frac{1}{\qPochhammer{q}{q}{n}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
beta[n] = (1)/(QPochhammer(q, q, n))

Subscript[\[Beta], n] == Divide[1,QPochhammer[q, q, n]]
Failure Failure Error
Failed [297 / 300]
Result: Complex[0.3660254037844387, -1.366025403784439]
Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[β, 1.5], Rule[Subscript[β, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[2.232050807568878, -0.8660254037844388]
Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[β, 1.5], Rule[Subscript[β, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
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