Results of q-Hypergeometric and Related Functions
| DLMF | Formula | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|
| 17.2.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{a}{q}{-n} = \frac{1}{\qPochhammer{aq^{-n}}{q}{n}}} | QPochhammer(a, q, - n) = (1)/(QPochhammer(a*(q)^(- n), q, n)) |
QPochhammer[a, q, - n] == Divide[1,QPochhammer[a*(q)^(- n), q, n]] |
Successful | Failure | - | Failed [18 / 180]
{Indeterminate <- {Rule[a, -1.5], Rule[n, 1], Rule[q, -1.5]}Indeterminate <- {Rule[a, -1.5], Rule[n, 2], Rule[q, -1.5]} |
| 17.2.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\qPochhammer{aq^{-n}}{q}{n}} = \frac{(-q/a)^{n}q^{\binom{n}{2}}}{\qPochhammer{q/a}{q}{n}}} | (1)/(QPochhammer(a*(q)^(- n), q, n)) = ((- q/ a)^(n)* (q)^(binomial(n,2)))/(QPochhammer(q/ a, q, n)) |
Divide[1,QPochhammer[a*(q)^(- n), q, n]] == Divide[(- q/ a)^(n)* (q)^(Binomial[n,2]),QPochhammer[q/ a, q, n]] |
Successful | Failure | - | Failed [18 / 180]
{Indeterminate <- {Rule[a, -1.5], Rule[n, 1], Rule[q, -1.5]}Indeterminate <- {Rule[a, -1.5], Rule[n, 2], Rule[q, -1.5]} |
| 17.2.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{a}{q}{\nu} = \prod_{j=0}^{\infty}\left(\frac{1-aq^{j}}{1-aq^{\nu+j}}\right)} | QPochhammer(a, q, nu) = product((1 - a*(q)^(j))/(1 - a*(q)^(nu + j)), j = 0..infinity) |
QPochhammer[a, q, \[Nu]] == Product[Divide[1 - a*(q)^(j),1 - a*(q)^(\[Nu]+ j)], {j, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Error | Failed [33 / 300]
{Indeterminate <- {Rule[a, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[a, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[ν, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.2.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{a}{q}{\infty} = \prod_{j=0}^{\infty}(1-aq^{j})} | QPochhammer(a, q, infinity) = product(1 - a*(q)^(j), j = 0..infinity) |
QPochhammer[a, q, Infinity] == Product[1 - a*(q)^(j), {j, 0, Infinity}, GenerateConditions->None] |
Failure | Failure | Error | Failed [48 / 60]
{Plus[Times[-1.0, QPochhammer[-1.5, Complex[0.8660254037844387, 0.49999999999999994]]], QPochhammer[-1.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]] <- {Rule[a, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[a, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.2.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{a}{q^{-1}}{n} = \qPochhammer{a^{-1}}{q}{n}(-a)^{n}q^{-\binom{n}{2}}} | QPochhammer(a, (q)^(- 1), n) = QPochhammer((a)^(- 1), q, n)*(- a)^(n)* (q)^(-binomial(n,2)) |
QPochhammer[a, (q)^(- 1), n] == QPochhammer[(a)^(- 1), q, n]*(- a)^(n)* (q)^(-Binomial[n,2]) |
Successful | Failure | - | Successful [Tested: 180] |
| 17.2.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\qPochhammer{a}{q^{-1}}{n}}{\qPochhammer{b}{q^{-1}}{n}} = \frac{\qPochhammer{a^{-1}}{q}{n}}{\qPochhammer{b^{-1}}{q}{n}}\left(\frac{a}{b}\right)^{n}} | (QPochhammer(a, (q)^(- 1), n))/(QPochhammer(b, (q)^(- 1), n)) = (QPochhammer((a)^(- 1), q, n))/(QPochhammer((b)^(- 1), q, n))*((a)/(b))^(n) |
Divide[QPochhammer[a, (q)^(- 1), n],QPochhammer[b, (q)^(- 1), n]] == Divide[QPochhammer[(a)^(- 1), q, n],QPochhammer[(b)^(- 1), q, n]]*(Divide[a,b])^(n) |
Successful | Failure | - | Failed [20 / 300]
{Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[q, -1.5]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 3], Rule[q, -1.5]} |
| 17.2.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{a}{q}{n} = \qPochhammer{q^{1-n}/a}{q}{n}(-a)^{n}q^{\binom{n}{2}}} | QPochhammer(a, q, n) = QPochhammer((q)^(1 - n)/ a, q, n)*(- a)^(n)* (q)^(binomial(n,2)) |
QPochhammer[a, q, n] == QPochhammer[(q)^(1 - n)/ a, q, n]*(- a)^(n)* (q)^(Binomial[n,2]) |
Successful | Failure | - | Successful [Tested: 180] |
| 17.2.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\qPochhammer{a}{q}{n}}{\qPochhammer{b}{q}{n}} = \frac{\qPochhammer{q^{1-n}/a}{q}{n}}{\qPochhammer{q^{1-n}/b}{q}{n}}\left(\frac{a}{b}\right)^{n}} | (QPochhammer(a, q, n))/(QPochhammer(b, q, n)) = (QPochhammer((q)^(1 - n)/ a, q, n))/(QPochhammer((q)^(1 - n)/ b, q, n))*((a)/(b))^(n) |
Divide[QPochhammer[a, q, n],QPochhammer[b, q, n]] == Divide[QPochhammer[(q)^(1 - n)/ a, q, n],QPochhammer[(q)^(1 - n)/ b, q, n]]*(Divide[a,b])^(n) |
Successful | Failure | - | Failed [12 / 300]
{Indeterminate <- {Rule[a, -1.5], Rule[b, -0.5], Rule[n, 2], Rule[q, -2]}Indeterminate <- {Rule[a, -1.5], Rule[b, -0.5], Rule[n, 3], Rule[q, -2]} |
| 17.2.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{aq^{-n}}{q}{n} = \qPochhammer{q/a}{q}{n}\left(-\frac{a}{q}\right)^{n}q^{-\binom{n}{2}}} | QPochhammer(a*(q)^(- n), q, n) = QPochhammer(q/ a, q, n)*(-(a)/(q))^(n)* (q)^(-binomial(n,2)) |
QPochhammer[a*(q)^(- n), q, n] == QPochhammer[q/ a, q, n]*(-Divide[a,q])^(n)* (q)^(-Binomial[n,2]) |
Successful | Failure | - | Successful [Tested: 180] |
| 17.2.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\qPochhammer{aq^{-n}}{q}{n}}{\qPochhammer{bq^{-n}}{q}{n}} = \frac{\qPochhammer{q/a}{q}{n}}{\qPochhammer{q/b}{q}{n}}\left(\frac{a}{b}\right)^{n}} | (QPochhammer(a*(q)^(- n), q, n))/(QPochhammer(b*(q)^(- n), q, n)) = (QPochhammer(q/ a, q, n))/(QPochhammer(q/ b, q, n))*((a)/(b))^(n) |
Divide[QPochhammer[a*(q)^(- n), q, n],QPochhammer[b*(q)^(- n), q, n]] == Divide[QPochhammer[q/ a, q, n],QPochhammer[q/ b, q, n]]*(Divide[a,b])^(n) |
Successful | Failure | - | Failed [30 / 300]
{Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[q, -1.5]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[q, -1.5]} |
| 17.2.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{a}{q}{n-k} = \frac{\qPochhammer{a}{q}{n}}{\qPochhammer{q^{1-n}/a}{q}{k}}\left(-\frac{q}{a}\right)^{k}q^{\binom{k}{2}-nk}} | QPochhammer(a, q, n - k) = (QPochhammer(a, q, n))/(QPochhammer((q)^(1 - n)/ a, q, k))*(-(q)/(a))^(k)* (q)^(binomial(k,2)- n*k) |
QPochhammer[a, q, n - k] == Divide[QPochhammer[a, q, n],QPochhammer[(q)^(1 - n)/ a, q, k]]*(-Divide[q,a])^(k)* (q)^(Binomial[k,2]- n*k) |
Successful | Failure | - | Failed [14 / 300]
{Indeterminate <- {Rule[a, -1.5], Rule[k, 2], Rule[n, 1], Rule[q, -1.5]}Indeterminate <- {Rule[a, -1.5], Rule[k, 3], Rule[n, 1], Rule[q, -1.5]} |
| 17.2.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\qPochhammer{a}{q}{n-k}}{\qPochhammer{b}{q}{n-k}} = \frac{\qPochhammer{a}{q}{n}}{\qPochhammer{b}{q}{n}}\frac{\qPochhammer{q^{1-n}/b}{q}{k}}{\qPochhammer{q^{1-n}/a}{q}{k}}\left(\frac{b}{a}\right)^{k}} | (QPochhammer(a, q, n - k))/(QPochhammer(b, q, n - k)) = (QPochhammer(a, q, n))/(QPochhammer(b, q, n))*(QPochhammer((q)^(1 - n)/ b, q, k))/(QPochhammer((q)^(1 - n)/ a, q, k))*((b)/(a))^(k) |
Divide[QPochhammer[a, q, n - k],QPochhammer[b, q, n - k]] == Divide[QPochhammer[a, q, n],QPochhammer[b, q, n]]*Divide[QPochhammer[(q)^(1 - n)/ b, q, k],QPochhammer[(q)^(1 - n)/ a, q, k]]*(Divide[b,a])^(k) |
Successful | Failure | - | Failed [15 / 300]
{Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 2], Rule[n, 1], Rule[q, -1.5]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 3], Rule[n, 1], Rule[q, -1.5]} |
| 17.2.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{aq^{-n}}{q}{k} = \frac{\qPochhammer{a}{q}{k}\qPochhammer{q/a}{q}{n}}{\qPochhammer{q^{1-k}/a}{q}{n}}q^{-nk}} | QPochhammer(a*(q)^(- n), q, k) = (QPochhammer(a, q, k)*QPochhammer(q/ a, q, n))/(QPochhammer((q)^(1 - k)/ a, q, n))*(q)^(- n*k) |
QPochhammer[a*(q)^(- n), q, k] == Divide[QPochhammer[a, q, k]*QPochhammer[q/ a, q, n],QPochhammer[(q)^(1 - k)/ a, q, n]]*(q)^(- n*k) |
Successful | Failure | - | Failed [14 / 300]
{Indeterminate <- {Rule[a, -1.5], Rule[k, 1], Rule[n, 2], Rule[q, -1.5]}Indeterminate <- {Rule[a, -1.5], Rule[k, 1], Rule[n, 3], Rule[q, -1.5]} |
| 17.2.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{aq^{-n}}{q}{n-k} = \frac{\qPochhammer{q/a}{q}{n}}{\qPochhammer{q/a}{q}{k}}\left(-\frac{a}{q}\right)^{n-k}q^{\binom{k}{2}-\binom{n}{2}}} | QPochhammer(a*(q)^(- n), q, n - k) = (QPochhammer(q/ a, q, n))/(QPochhammer(q/ a, q, k))*(-(a)/(q))^(n - k)* (q)^(binomial(k,2)-binomial(n,2)) |
QPochhammer[a*(q)^(- n), q, n - k] == Divide[QPochhammer[q/ a, q, n],QPochhammer[q/ a, q, k]]*(-Divide[a,q])^(n - k)* (q)^(Binomial[k,2]-Binomial[n,2]) |
Successful | Failure | - | Failed [27 / 300]
{Indeterminate <- {Rule[a, -1.5], Rule[k, 1], Rule[n, 1], Rule[q, -1.5]}Indeterminate <- {Rule[a, -1.5], Rule[k, 1], Rule[n, 2], Rule[q, -1.5]} |
| 17.2.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{aq^{n}}{q}{k} = \frac{\qPochhammer{a}{q}{k}\qPochhammer{aq^{k}}{q}{n}}{\qPochhammer{a}{q}{n}}} | QPochhammer(a*(q)^(n), q, k) = (QPochhammer(a, q, k)*QPochhammer(a*(q)^(k), q, n))/(QPochhammer(a, q, n)) |
QPochhammer[a*(q)^(n), q, k] == Divide[QPochhammer[a, q, k]*QPochhammer[a*(q)^(k), q, n],QPochhammer[a, q, n]] |
Successful | Failure | - | Failed [6 / 300]
{Indeterminate <- {Rule[a, -0.5], Rule[k, 1], Rule[n, 2], Rule[q, -2]}Indeterminate <- {Rule[a, -0.5], Rule[k, 1], Rule[n, 3], Rule[q, -2]} |
| 17.2.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{aq^{k}}{q}{n-k} = \frac{\qPochhammer{a}{q}{n}}{\qPochhammer{a}{q}{k}}} | QPochhammer(a*(q)^(k), q, n - k) = (QPochhammer(a, q, n))/(QPochhammer(a, q, k)) |
QPochhammer[a*(q)^(k), q, n - k] == Divide[QPochhammer[a, q, n],QPochhammer[a, q, k]] |
Successful | Failure | - | Failed [6 / 300]
{Indeterminate <- {Rule[a, -0.5], Rule[k, 2], Rule[n, 1], Rule[q, -2]}Indeterminate <- {Rule[a, -0.5], Rule[k, 2], Rule[n, 2], Rule[q, -2]} |
| 17.2.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{a}{q}{2n} = \qmultiPochhammersym{a,aq}{q^{2}}{n}} | Error |
QPochhammer[a, q, 2*n] == Product[QPochhammer[Part[{a , a*q},i],(q)^(2),n],{i,1,Length[{a , a*q}]}] |
Error | Failure | - | Successful [Tested: 180] |
| 17.2.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qPochhammer{a^{2}}{q^{2}}{n} = \qPochhammer{a}{q}{n}\qPochhammer{-a}{q}{n}} | QPochhammer((a)^(2), (q)^(2), n) = QPochhammer(a, q, n)*QPochhammer(- a, q, n) |
QPochhammer[(a)^(2), (q)^(2), n] == QPochhammer[a, q, n]*QPochhammer[- a, q, n] |
Successful | Successful | - | Successful [Tested: 180] |
| 17.2.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\qmultiPochhammersym{qa^{\frac{1}{2}},-qa^{\frac{1}{2}}}{q}{n}}{\qmultiPochhammersym{a^{\frac{1}{2}},-a^{\frac{1}{2}}}{q}{n}} = \frac{\qPochhammer{aq^{2}}{q^{2}}{n}}{\qPochhammer{a}{q^{2}}{n}}} | Error |
Divide[Product[QPochhammer[Part[{q*(a)^(Divide[1,2]), - q*(a)^(Divide[1,2])},i],q,n],{i,1,Length[{q*(a)^(Divide[1,2]), - q*(a)^(Divide[1,2])}]}],Product[QPochhammer[Part[{(a)^(Divide[1,2]), - (a)^(Divide[1,2])},i],q,n],{i,1,Length[{(a)^(Divide[1,2]), - (a)^(Divide[1,2])}]}]] == Divide[QPochhammer[a*(q)^(2), (q)^(2), n],QPochhammer[a, (q)^(2), n]] |
Error | Successful | - | Successful [Tested: 180] |
| 17.2.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\qPochhammer{aq^{2}}{q^{2}}{n}}{\qPochhammer{a}{q^{2}}{n}} = \frac{1-aq^{2n}}{1-a}} | (QPochhammer(a*(q)^(2), (q)^(2), n))/(QPochhammer(a, (q)^(2), n)) = (1 - a*(q)^(2*n))/(1 - a) |
Divide[QPochhammer[a*(q)^(2), (q)^(2), n],QPochhammer[a, (q)^(2), n]] == Divide[1 - a*(q)^(2*n),1 - a] |
Successful | Failure | - | Successful [Tested: 180] |
| 17.2.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\qPochhammer{aq^{k}}{q^{k}}{n}}{\qPochhammer{a}{q^{k}}{n}} = \frac{1-aq^{kn}}{1-a}} | (QPochhammer(a*(q)^(k), (q)^(k), n))/(QPochhammer(a, (q)^(k), n)) = (1 - a*(q)^(k*n))/(1 - a) |
Divide[QPochhammer[a*(q)^(k), (q)^(k), n],QPochhammer[a, (q)^(k), n]] == Divide[1 - a*(q)^(k*n),1 - a] |
Error | Failure | - | Failed [2 / 300]
{Indeterminate <- {Rule[a, -0.5], Rule[k, 1], Rule[n, 2], Rule[q, -2]}Indeterminate <- {Rule[a, -0.5], Rule[k, 1], Rule[n, 3], Rule[q, -2]} |
| 17.2.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{\tau\to 0}\qPochhammer{a/\tau}{q}{n}\tau^{n} = \lim_{\sigma\to\infty}\qPochhammer{a\sigma}{q}{n}\sigma^{-n}} | limit(QPochhammer(a/ tau, q, n)*(tau)^(n), tau = 0) = limit(QPochhammer(a*sigma, q, n)*(sigma)^(- n), sigma = infinity) |
Limit[QPochhammer[a/ \[Tau], q, n]*\[Tau]^(n), \[Tau] -> 0, GenerateConditions->None] == Limit[QPochhammer[a*\[Sigma], q, n]*\[Sigma]^(- n), \[Sigma] -> Infinity, GenerateConditions->None] |
Failure | Failure | Error | Successful [Tested: 180] |
| 17.2.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{\sigma\to\infty}\qPochhammer{a\sigma}{q}{n}\sigma^{-n} = (-a)^{n}q^{\binom{n}{2}}} | limit(QPochhammer(a*sigma, q, n)*(sigma)^(- n), sigma = infinity) = (- a)^(n)* (q)^(binomial(n,2)) |
Limit[QPochhammer[a*\[Sigma], q, n]*\[Sigma]^(- n), \[Sigma] -> Infinity, GenerateConditions->None] == (- a)^(n)* (q)^(Binomial[n,2]) |
Failure | Failure | Error | Successful [Tested: 180] |
| 17.2.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{\tau\to 0}\frac{\qPochhammer{a/\tau}{q}{n}}{\qPochhammer{b/\tau}{q}{n}} = \lim_{\sigma\to\infty}\frac{\qPochhammer{a\sigma}{q}{n}}{\qPochhammer{b\sigma}{q}{n}}} | limit((QPochhammer(a/ tau, q, n))/(QPochhammer(b/ tau, q, n)), tau = 0) = limit((QPochhammer(a*sigma, q, n))/(QPochhammer(b*sigma, q, n)), sigma = infinity) |
Limit[Divide[QPochhammer[a/ \[Tau], q, n],QPochhammer[b/ \[Tau], q, n]], \[Tau] -> 0, GenerateConditions->None] == Limit[Divide[QPochhammer[a*\[Sigma], q, n],QPochhammer[b*\[Sigma], q, n]], \[Sigma] -> Infinity, GenerateConditions->None] |
Failure | Failure | Error | Successful [Tested: 300] |
| 17.2.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{\sigma\to\infty}\frac{\qPochhammer{a\sigma}{q}{n}}{\qPochhammer{b\sigma}{q}{n}} = \left(\frac{a}{b}\right)^{n}} | limit((QPochhammer(a*sigma, q, n))/(QPochhammer(b*sigma, q, n)), sigma = infinity) = ((a)/(b))^(n) |
Limit[Divide[QPochhammer[a*\[Sigma], q, n],QPochhammer[b*\[Sigma], q, n]], \[Sigma] -> Infinity, GenerateConditions->None] == (Divide[a,b])^(n) |
Failure | Failure | Error | Successful [Tested: 300] |
| 17.2.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{\tau\to 0}\frac{\qPochhammer{a/\tau}{q}{n}\qPochhammer{b/\tau}{q}{n}}{\qPochhammer{c/\tau^{2}}{q}{n}} = (-1)^{n}\left(\frac{ab}{c}\right)^{n}q^{\binom{n}{2}}} | limit((QPochhammer(a/ tau, q, n)*QPochhammer(b/ tau, q, n))/(QPochhammer(c/ (tau)^(2), q, n)), tau = 0) = (- 1)^(n)*((a*b)/(c))^(n)* (q)^(binomial(n,2)) |
Limit[Divide[QPochhammer[a/ \[Tau], q, n]*QPochhammer[b/ \[Tau], q, n],QPochhammer[c/ \[Tau]^(2), q, n]], \[Tau] -> 0, GenerateConditions->None] == (- 1)^(n)*(Divide[a*b,c])^(n)* (q)^(Binomial[n,2]) |
Error | Failure | - | Successful [Tested: 300] |
| 17.2.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qbinom{n}{m}{q} = \frac{\qPochhammer{q}{q}{n}}{\qPochhammer{q}{q}{m}\qPochhammer{q}{q}{n-m}}\\} | QBinomial(n, m, q) = (QPochhammer(q, q, n))/(QPochhammer(q, q, m)*QPochhammer(q, q, n - m)) |
QBinomial[n,m,q] == Divide[QPochhammer[q, q, n],QPochhammer[q, q, m]*QPochhammer[q, q, n - m]] |
Successful | Failure | - | Failed [1 / 90]
{Complex[-0.058394160583941646, 0.1605839416058394] <- {Rule[m, 3], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.2.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\qPochhammer{q}{q}{n}}{\qPochhammer{q}{q}{m}\qPochhammer{q}{q}{n-m}}\\ = \frac{\qPochhammer{q^{-n}}{q}{m}(-1)^{m}q^{nm-\binom{m}{2}}}{\qPochhammer{q}{q}{m}}} | (QPochhammer(q, q, n))/(QPochhammer(q, q, m)*QPochhammer(q, q, n - m)) = (QPochhammer((q)^(- n), q, m)*(- 1)^(m)* (q)^(n*m -binomial(m,2)))/(QPochhammer(q, q, m)) |
Divide[QPochhammer[q, q, n],QPochhammer[q, q, m]*QPochhammer[q, q, n - m]] == Divide[QPochhammer[(q)^(- n), q, m]*(- 1)^(m)* (q)^(n*m -Binomial[m,2]),QPochhammer[q, q, m]] |
Successful | Failure | - | Failed [3 / 90]
{Complex[0.11678832116788332, -0.3211678832116788] <- {Rule[m, 3], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}Complex[1.0, 0.0] <- {Rule[m, 3], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.2.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{q\to 1}\qbinom{n}{m}{q} = \binom{n}{m}} | limit(QBinomial(n, m, q), q = 1) = binomial(n,m) |
Limit[QBinomial[n,m,q], q -> 1, GenerateConditions->None] == Binomial[n,m] |
Failure | Error | Error | Skipped - Because timed out |
| 17.2.E28 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{n}{m} = \frac{n!}{m!(n-m)!}} | binomial(n,m) = (factorial(n))/(factorial(m)*factorial(n - m)) |
Binomial[n,m] == Divide[(n)!,(m)!*(n - m)!] |
Successful | Successful | Skip - symbolical successful subtest | Successful [Tested: 9] |
| 17.2.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qbinom{m+n}{m}{q} = \frac{\qPochhammer{q^{n+1}}{q}{m}}{\qPochhammer{q}{q}{m}}} | QBinomial(m + n, m, q) = (QPochhammer((q)^(n + 1), q, m))/(QPochhammer(q, q, m)) |
QBinomial[m + n,m,q] == Divide[QPochhammer[(q)^(n + 1), q, m],QPochhammer[q, q, m]] |
Successful | Failure | - | Failed [3 / 90]
{Complex[0.9416058394160581, 0.1605839416058394] <- {Rule[m, 3], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}Complex[1.0, 0.0] <- {Rule[m, 3], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.2.E30 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qbinom{-n}{m}{q} = \qbinom{m+n-1}{m}{q}(-1)^{m}q^{-mn-\binom{m}{2}}} | QBinomial(- n, m, q) = QBinomial(m + n - 1, m, q)*(- 1)^(m)* (q)^(- m*n -binomial(m,2)) |
QBinomial[- n,m,q] == QBinomial[m + n - 1,m,q]*(- 1)^(m)* (q)^(- m*n -Binomial[m,2]) |
Failure | Failure | Error | Failed [84 / 90]
{Complex[0.7320508075688774, 0.0] <- {Rule[m, 1], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Complex[-2.3660254037844384, -1.3660254037844386] <- {Rule[m, 1], Rule[n, 3], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.2.E31 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qbinom{n}{m}{q} = \qbinom{n-1}{m-1}{q}+q^{m}\qbinom{n-1}{m}{q}} | QBinomial(n, m, q) = QBinomial(n - 1, m - 1, q)+ (q)^(m)* QBinomial(n - 1, m, q) |
QBinomial[n,m,q] == QBinomial[n - 1,m - 1,q]+ (q)^(m)* QBinomial[n - 1,m,q] |
Successful | Failure | - | Successful [Tested: 90] |
| 17.2.E32 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qbinom{n}{m}{q} = \qbinom{n-1}{m}{q}+q^{n-m}\qbinom{n-1}{m-1}{q}} | QBinomial(n, m, q) = QBinomial(n - 1, m, q)+ (q)^(n - m)* QBinomial(n - 1, m - 1, q) |
QBinomial[n,m,q] == QBinomial[n - 1,m,q]+ (q)^(n - m)* QBinomial[n - 1,m - 1,q] |
Successful | Failure | - | Successful [Tested: 90] |
| 17.2.E33 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\qbinom{n}{m}{q} = \frac{1}{\qPochhammer{q}{q}{m}}} | limit(QBinomial(n, m, q), n = infinity) = (1)/(QPochhammer(q, q, m)) |
Limit[QBinomial[n,m,q], n -> Infinity, GenerateConditions->None] == Divide[1,QPochhammer[q, q, m]] |
Failure | Failure | Error | Failed [24 / 30]
{Plus[Complex[-0.5, -1.866025403784439], Times[Complex[-0.5, -1.866025403784439], Plus[-1.0, Power[2.718281828459045, Times[Complex[0.0, 2.0], Interval[{-2.2250738585072014*^-308, 3.1415926535897936}]]]]]] <- {Rule[m, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[1.3660254037844395, -1.3660254037844388], Times[Complex[0.5000000000000009, -1.866025403784439], Plus[-1.0, Power[2.718281828459045, Times[Complex[0.0, 2.0], Interval[{-2.2250738585072014*^-308, 3.1415926535897936}]]]], Plus[Complex[0.8660254037844387, 0.49999999999999994], Power[2.718281828459045, Times[Complex[0.0, 2.0], Interval[{-2.2250738585072014*^-308, 3.1415926535897936}]]]]]] <- {Rule[m, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.2.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{n\to\infty}\qbinom{rn+u}{sn+t}{q} = \frac{1}{\qPochhammer{q}{q}{\infty}}} | limit(QBinomial(r*n + u, sn(+)*t, q), n = infinity) = (1)/(QPochhammer(q, q, infinity)) |
Limit[QBinomial[r*n + u,sn(+)*t,q], n -> Infinity, GenerateConditions->None] == Divide[1,QPochhammer[q, q, Infinity]] |
Error | Failure | Skip - symbolical successful subtest | Error |
| 17.2.E34 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{1}{\qPochhammer{q}{q}{\infty}} = \prod_{j=1}^{\infty}\frac{1}{(1-q^{j})}} | (1)/(QPochhammer(q, q, infinity)) = product((1)/(1 - (q)^(j)), j = 1..infinity) |
Divide[1,QPochhammer[q, q, Infinity]] == Product[Divide[1,1 - (q)^(j)], {j, 1, Infinity}, GenerateConditions->None] |
Failure | Failure | Error | Failed [7 / 10]
{Plus[Times[-1.0, Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], -1]], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]] <- {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Times[-1.0, Power[QPochhammer[Complex[0.5000000000000001, -0.8660254037844386], Complex[0.5000000000000001, -0.8660254037844386]], -1]], Power[QPochhammer[Complex[0.5000000000000001, -0.8660254037844386], Complex[0.5000000000000001, -0.8660254037844386], DirectedInfinity[1]], -1]] <- {Rule[q, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]} |
| 17.2.E35 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{j=0}^{n}\qbinom{n}{j}{q}(-z)^{j}q^{\binom{j}{2}} = \qPochhammer{z}{q}{n}} | sum(QBinomial(n, j, q)*(- z)^(j)* (q)^(binomial(j,2)), j = 0..n) = QPochhammer(z, q, n) |
Sum[QBinomial[n,j,q]*(- z)^(j)* (q)^(Binomial[j,2]), {j, 0, n}, GenerateConditions->None] == QPochhammer[z, q, n] |
Failure | Successful | Error | Successful [Tested: 210] |
| 17.2.E36 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{j=0}^{n}\binom{n}{j}(-z)^{j} = (1-z)^{n}} | sum(binomial(n,j)*(- z)^(j), j = 0..n) = (1 - z)^(n) |
Sum[Binomial[n,j]*(- z)^(j), {j, 0, n}, GenerateConditions->None] == (1 - z)^(n) |
Successful | Successful | - | Successful [Tested: 21] |
| 17.2.E37 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\frac{\qPochhammer{a}{q}{n}}{\qPochhammer{q}{q}{n}}z^{n} = \frac{\qPochhammer{az}{q}{\infty}}{\qPochhammer{z}{q}{\infty}}} | sum((QPochhammer(a, q, n))/(QPochhammer(q, q, n))*(z)^(n), n = 0..infinity) = (QPochhammer(a*z, q, infinity))/(QPochhammer(z, q, infinity)) |
Sum[Divide[QPochhammer[a, q, n],QPochhammer[q, q, n]]*(z)^(n), {n, 0, Infinity}, GenerateConditions->None] == Divide[QPochhammer[a*z, q, Infinity],QPochhammer[z, q, Infinity]] |
Failure | Failure | Error | Failed [240 / 300]
{Plus[Times[QPochhammer[Complex[-1.299038105676658, -0.7499999999999999], Complex[0.8660254037844387, 0.49999999999999994]], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], -1]], Times[-1.0, QPochhammer[Complex[-1.299038105676658, -0.7499999999999999], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]]] <- {Rule[a, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Times[Power[QPochhammer[Complex[-0.4999999999999998, 0.8660254037844387], Complex[0.8660254037844387, 0.49999999999999994]], -1], QPochhammer[Complex[0.7499999999999997, -1.299038105676658], Complex[0.8660254037844387, 0.49999999999999994]]], Times[-1.0, Power[QPochhammer[Complex[-0.4999999999999998, 0.8660254037844387], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[0.7499999999999997, -1.299038105676658], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]] <- {Rule[a, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.2.E38 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\qbinom{n+m}{n}{q}z^{n} = \frac{1}{\qPochhammer{z}{q}{m+1}}} | sum(QBinomial(n + m, n, q)*(z)^(n), n = 0..infinity) = (1)/(QPochhammer(z, q, m + 1)) |
Sum[QBinomial[n + m,n,q]*(z)^(n), {n, 0, Infinity}, GenerateConditions->None] == Divide[1,QPochhammer[z, q, m + 1]] |
Failure | Error | Error | Skipped - Because timed out |
| 17.2.E39 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{j=0}^{n}\qbinom{n}{j}{q^{2}}q^{j} = \qPochhammer{-q}{q}{n}} | sum(QBinomial(n, j, (q)^(2))*(q)^(j), j = 0..n) = QPochhammer(- q, q, n) |
Sum[QBinomial[n,j,(q)^(2)]*(q)^(j), {j, 0, n}, GenerateConditions->None] == QPochhammer[- q, q, n] |
Failure | Error | Error | Successful [Tested: 30] |
| 17.2.E40 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{j=0}^{2n}(-1)^{j}\qbinom{2n}{j}{q} = \qPochhammer{q}{q^{2}}{n}} | sum((- 1)^(j)* QBinomial(2*n, j, q), j = 0..2*n) = QPochhammer(q, (q)^(2), n) |
Sum[(- 1)^(j)* QBinomial[2*n,j,q], {j, 0, 2*n}, GenerateConditions->None] == QPochhammer[q, (q)^(2), n] |
Failure | Successful | Error | Successful [Tested: 30] |
| 17.3.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\frac{(1-q)^{n}x^{n}}{\qPochhammer{q}{q}{n}} = \frac{1}{\qPochhammer{(1-q)x}{q}{\infty}}} | sum(((1 - q)^(n)* (x)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = (1)/(QPochhammer((1 - q)* x, q, infinity)) |
Sum[Divide[(1 - q)^(n)* (x)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == Divide[1,QPochhammer[(1 - q)* x, q, Infinity]] |
Failure | Error | Error | Skipped - Because timed out |
| 17.3.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\frac{(1-q)^{n}q^{\binom{n}{2}}x^{n}}{\qPochhammer{q}{q}{n}} = \qPochhammer{-(1-q)x}{q}{\infty}} | sum(((1 - q)^(n)* (q)^(binomial(n,2))* (x)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = QPochhammer(-(1 - q)* x, q, infinity) |
Sum[Divide[(1 - q)^(n)* (q)^(Binomial[n,2])* (x)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == QPochhammer[-(1 - q)* x, q, Infinity] |
Failure | Error | Error | Skipped - Because timed out |
| 17.4.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{0}q = a_{1}b_{1}} | a[0]*q = a[1]*b[1] |
Subscript[a, 0]*q == Subscript[a, 1]*Subscript[b, 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 17.4.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b_{1} = -b_{2}} | b[1] = - b[2] |
Subscript[b, 1] == - Subscript[b, 2] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 17.4.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{0}q = a_{1}b_{1}} | a[0]*q = a[1]*b[1] |
Subscript[a, 0]*q == Subscript[a, 1]*Subscript[b, 1] |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 17.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{0}{0}@{-}{-}{q}{z} = \sum_{n=0}^{\infty}\frac{(-1)^{n}q^{\binom{n}{2}}z^{n}}{\qPochhammer{q}{q}{n}}} | Error |
QHypergeometricPFQ[{-},{-},q,z] == Sum[Divide[(- 1)^(n)* (q)^(Binomial[n,2])* (z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] |
Error | Failure | Skip - symbolical successful subtest | Error |
| 17.5.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\frac{(-1)^{n}q^{\binom{n}{2}}z^{n}}{\qPochhammer{q}{q}{n}} = \qPochhammer{z}{q}{\infty}} | sum(((- 1)^(n)* (q)^(binomial(n,2))* (z)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = QPochhammer(z, q, infinity) |
Sum[Divide[(- 1)^(n)* (q)^(Binomial[n,2])* (z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == QPochhammer[z, q, Infinity] |
Failure | Failure | Error | Failed [8 / 10]
{Plus[QPochhammer[0.5, Complex[0.8660254037844387, 0.49999999999999994]], Times[-1.0, QPochhammer[0.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]] <- {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, 0.5]}Indeterminate <- {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[z, 0.5]} |
| 17.5.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{1}{0}@{a}{-}{q}{z} = \frac{\qPochhammer{az}{q}{\infty}}{\qPochhammer{z}{q}{\infty}}} | Error |
QHypergeometricPFQ[{a},{-},q,z] == Divide[QPochhammer[a*z, q, Infinity],QPochhammer[z, q, Infinity]] |
Error | Failure | - | Error |
| 17.5.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{1}{0}@{q^{-n}}{-}{q}{z} = \qPochhammer{zq^{-n}}{q}{n}} | Error |
QHypergeometricPFQ[{(q)^(- n)},{-},q,z] == QPochhammer[z*(q)^(- n), q, n] |
Error | Failure | - | Error |
| 17.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{1}{0}@{0}{-}{q}{z} = \sum_{n=0}^{\infty}\frac{z^{n}}{\qPochhammer{q}{q}{n}}} | Error |
QHypergeometricPFQ[{0},{-},q,z] == Sum[Divide[(z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] |
Error | Failure | Skip - symbolical successful subtest | Error |
| 17.5.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\frac{z^{n}}{\qPochhammer{q}{q}{n}} = \frac{1}{\qPochhammer{z}{q}{\infty}}} | sum(((z)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = (1)/(QPochhammer(z, q, infinity)) |
Sum[Divide[(z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == Divide[1,QPochhammer[z, q, Infinity]] |
Failure | Failure | Error | Failed [8 / 10]
{Plus[QHypergeometricPFQ[{0.0} <- {}, Complex[0.8660254037844387, 0.49999999999999994], 0.5], Times[-1.0, Power[QPochhammer[0.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, 0.5]}QHypergeometricPFQ[{0.0} <- {}, Complex[-0.4999999999999998, 0.8660254037844387], 0.5], {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[z, 0.5]} |
| 17.5.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{1}{1}@@{a}{c}{q}{c/a} = \frac{\qPochhammer{c/a}{q}{\infty}}{\qPochhammer{c}{q}{\infty}}} | Error |
QHypergeometricPFQ[{a},{c},q,c/ a] == Divide[QPochhammer[c/ a, q, Infinity],QPochhammer[c, q, Infinity]] |
Error | Failure | - | Failed [96 / 120]
{Plus[QHypergeometricPFQ[{-1.5} <- {-0.5}, Complex[0.8660254037844387, 0.49999999999999994], 0.3333333333333333], Times[-1.0, Power[QPochhammer[-0.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[0.3333333333333333, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]], {Rule[a, -1.5], Rule[c, -0.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[a, -1.5], Rule[c, -0.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.6.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{a,b}{c}{q}{\ifrac{c}{(ab)}} = \frac{\qmultiPochhammersym{c/a,c/b}{q}{\infty}}{\qmultiPochhammersym{c,c/(ab)}{q}{\infty}}} | Error |
QHypergeometricPFQ[{a , b},{c},q,Divide[c,a*b]] == Divide[Product[QPochhammer[Part[{c/ a , c/ b},i],q,Infinity],{i,1,Length[{c/ a , c/ b}]}],Product[QPochhammer[Part[{c , c/(a*b)},i],q,Infinity],{i,1,Length[{c , c/(a*b)}]}]] |
Error | Failure | - | Failed [262 / 300]
{Plus[0.0, QHypergeometricPFQ[{-1.5, -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], -0.6666666666666666]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[0.0, QHypergeometricPFQ[{-1.5, -1.5} <- {-1.5}, Complex[-0.4999999999999998, 0.8660254037844387], -0.6666666666666666]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.6.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{a,q^{-n}}{c}{q}{\ifrac{cq^{n}}{a}} = \frac{\qPochhammer{c/a}{q}{n}}{\qPochhammer{c}{q}{n}}} | Error |
QHypergeometricPFQ[{a , (q)^(- n)},{c},q,Divide[c*(q)^(n),a]] == Divide[QPochhammer[c/ a, q, n],QPochhammer[c, q, n]] |
Error | Failure | - | Failed [204 / 300]
{Plus[0.0, QHypergeometricPFQ[{-1.5, Complex[0.8660254037844387, -0.49999999999999994]} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[a, -1.5], Rule[c, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[0.5000000000000001, -0.8660254037844386]} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.5000000000000001, 0.8660254037844386]]], {Rule[a, -1.5], Rule[c, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.6.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{a,q^{-n}}{c}{q}{q} = \frac{a^{n}\qPochhammer{c/a}{q}{n}}{\qPochhammer{c}{q}{n}}} | Error |
QHypergeometricPFQ[{a , (q)^(- n)},{c},q,q] == Divide[(a)^(n)* QPochhammer[c/ a, q, n],QPochhammer[c, q, n]] |
Error | Failure | - | Failed [168 / 300]
{Plus[0.0, QHypergeometricPFQ[{-1.5, Complex[0.8660254037844387, -0.49999999999999994]} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[a, -1.5], Rule[c, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[0.5000000000000001, -0.8660254037844386]} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[a, -1.5], Rule[c, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.6.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{b^{2},\ifrac{b^{2}}{c}}{c}{q^{2}}{\ifrac{cq}{b^{2}}} = \frac{1}{2}\frac{\qmultiPochhammersym{b^{2},q}{q^{2}}{\infty}}{\qmultiPochhammersym{c,cq/b^{2}}{q^{2}}{\infty}}\left(\frac{\qPochhammer{c/b}{q}{\infty}}{\qPochhammer{b}{q}{\infty}}+\frac{\qPochhammer{-c/b}{q}{\infty}}{\qPochhammer{-b}{q}{\infty}}\right)} | Error |
QHypergeometricPFQ[{(b)^(2),Divide[(b)^(2),c]},{c},(q)^(2),Divide[c*q,(b)^(2)]] == Divide[1,2]*Divide[Product[QPochhammer[Part[{(b)^(2), q},i],(q)^(2),Infinity],{i,1,Length[{(b)^(2), q}]}],Product[QPochhammer[Part[{c , c*q/ (b)^(2)},i],(q)^(2),Infinity],{i,1,Length[{c , c*q/ (b)^(2)}]}]]*(Divide[QPochhammer[c/ b, q, Infinity],QPochhammer[b, q, Infinity]]+Divide[QPochhammer[- c/ b, q, Infinity],QPochhammer[- b, q, Infinity]]) |
Error | Failure | - | Skipped - Because timed out |
| 17.6.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{a,b}{aq/b}{q}{-q/b} = \frac{\qPochhammer{-q}{q}{\infty}\qmultiPochhammersym{aq,\ifrac{aq^{2}}{b^{2}}}{q^{2}}{\infty}}{\qmultiPochhammersym{-q/b,aq/b}{q}{\infty}}} | Error |
QHypergeometricPFQ[{a , b},{a*q/ b},q,- q/ b] == Divide[QPochhammer[- q, q, Infinity]*Product[QPochhammer[Part[{a*q ,Divide[a*(q)^(2),(b)^(2)]},i],(q)^(2),Infinity],{i,1,Length[{a*q ,Divide[a*(q)^(2),(b)^(2)]}]}],Product[QPochhammer[Part[{- q/ b , a*q/ b},i],q,Infinity],{i,1,Length[{- q/ b , a*q/ b}]}]] |
Error | Failure | - | Skipped - Because timed out |
| 17.6.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{a,b}{c}{q}{z} = \frac{\qmultiPochhammersym{b,az}{q}{\infty}}{\qmultiPochhammersym{c,z}{q}{\infty}}\qgenhyperphi{2}{1}@@{c/b,z}{az}{q}{b}} | Error |
QHypergeometricPFQ[{a , b},{c},q,z] == Divide[Product[QPochhammer[Part[{b , a*z},i],q,Infinity],{i,1,Length[{b , a*z}]}],Product[QPochhammer[Part[{c , z},i],q,Infinity],{i,1,Length[{c , z}]}]]*QHypergeometricPFQ[{c/ b , z},{a*z},q,b] |
Error | Failure | - | Skip - No test values generated |
| 17.6.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{a,b}{c}{q}{z} = \frac{\qmultiPochhammersym{c/b,bz}{q}{\infty}}{\qmultiPochhammersym{c,z}{q}{\infty}}\qgenhyperphi{2}{1}@@{\ifrac{abz}{c},b}{bz}{q}{c/b}} | Error |
QHypergeometricPFQ[{a , b},{c},q,z] == Divide[Product[QPochhammer[Part[{c/ b , b*z},i],q,Infinity],{i,1,Length[{c/ b , b*z}]}],Product[QPochhammer[Part[{c , z},i],q,Infinity],{i,1,Length[{c , z}]}]]*QHypergeometricPFQ[{Divide[a*b*z,c], b},{b*z},q,c/ b] |
Error | Failure | - | Skip - No test values generated |
| 17.6.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{a,b}{c}{q}{z} = \frac{\qPochhammer{\ifrac{abz}{c}}{q}{\infty}}{\qPochhammer{z}{q}{\infty}}\qgenhyperphi{2}{1}@@{c/a,c/b}{c}{q}{\ifrac{abz}{c}}} | Error |
QHypergeometricPFQ[{a , b},{c},q,z] == Divide[QPochhammer[Divide[a*b*z,c], q, Infinity],QPochhammer[z, q, Infinity]]*QHypergeometricPFQ[{c/ a , c/ b},{c},q,Divide[a*b*z,c]] |
Error | Failure | - | Skip - No test values generated |
| 17.6.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@{a,b}{c}{q}{q}+\frac{\qmultiPochhammersym{q/c,a,b}{q}{\infty}}{\qmultiPochhammersym{c/q,aq/c,bq/c}{q}{\infty}}\qgenhyperphi{2}{1}@{aq/c,bq/c}{q^{2}/c}{q}{q} = \frac{\qmultiPochhammersym{q/c,abq/c}{q}{\infty}}{\qmultiPochhammersym{aq/c,bq/c}{q}{\infty}}} | Error |
QHypergeometricPFQ[{a , b},{c},q,q]+Divide[Product[QPochhammer[Part[{q/ c , a , b},i],q,Infinity],{i,1,Length[{q/ c , a , b}]}],Product[QPochhammer[Part[{c/ q , a*q/ c , b*q/ c},i],q,Infinity],{i,1,Length[{c/ q , a*q/ c , b*q/ c}]}]]*QHypergeometricPFQ[{a*q/ c , b*q/ c},{(q)^(2)/ c},q,q] == Divide[Product[QPochhammer[Part[{q/ c , a*b*q/ c},i],q,Infinity],{i,1,Length[{q/ c , a*b*q/ c}]}],Product[QPochhammer[Part[{a*q/ c , b*q/ c},i],q,Infinity],{i,1,Length[{a*q/ c , b*q/ c}]}]] |
Error | Failure | - | Skipped - Because timed out |
| 17.6.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{a,b}{c}{q}{z} = \frac{\qmultiPochhammersym{abz/c,q/c}{q}{\infty}}{\qmultiPochhammersym{az/c,q/a}{q}{\infty}}\qgenhyperphi{2}{1}@@{c/a,cq/(abz)}{cq/(az)}{q}{bq/c}-\frac{\qmultiPochhammersym{b,q/c,c/a,az/q,q^{2}/(az)}{q}{\infty}}{\qmultiPochhammersym{c/q,bq/c,q/a,az/c,cq/(az)}{q}{\infty}}\qgenhyperphi{2}{1}@@{aq/c,bq/c}{q^{2}/c}{q}{z}} | Error |
QHypergeometricPFQ[{a , b},{c},q,z] == Divide[Product[QPochhammer[Part[{a*b*z/ c , q/ c},i],q,Infinity],{i,1,Length[{a*b*z/ c , q/ c}]}],Product[QPochhammer[Part[{a*z/ c , q/ a},i],q,Infinity],{i,1,Length[{a*z/ c , q/ a}]}]]*QHypergeometricPFQ[{c/ a , c*q/(a*b*z)},{c*q/(a*z)},q,b*q/ c]-Divide[Product[QPochhammer[Part[{b , q/ c , c/ a , a*z/ q , (q)^(2)/(a*z)},i],q,Infinity],{i,1,Length[{b , q/ c , c/ a , a*z/ q , (q)^(2)/(a*z)}]}],Product[QPochhammer[Part[{c/ q , b*q/ c , q/ a , a*z/ c , c*q/(a*z)},i],q,Infinity],{i,1,Length[{c/ q , b*q/ c , q/ a , a*z/ c , c*q/(a*z)}]}]]*QHypergeometricPFQ[{a*q/ c , b*q/ c},{(q)^(2)/ c},q,z] |
Error | Failure | - | Skip - No test values generated |
| 17.6.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{a,b}{c}{q}{z} = \frac{\qmultiPochhammersym{b,c/a,az,q/(az)}{q}{\infty}}{\qmultiPochhammersym{c,b/a,z,q/z}{q}{\infty}}\qgenhyperphi{2}{1}@@{a,aq/c}{aq/b}{q}{cq/(abz)}+\frac{\qmultiPochhammersym{a,c/b,bz,q/(bz)}{q}{\infty}}{\qmultiPochhammersym{c,a/b,z,q/z}{q}{\infty}}\qgenhyperphi{2}{1}@@{b,bq/c}{bq/a}{q}{cq/(abz)}} | Error |
QHypergeometricPFQ[{a , b},{c},q,z] == Divide[Product[QPochhammer[Part[{b , c/ a , a*z , q/(a*z)},i],q,Infinity],{i,1,Length[{b , c/ a , a*z , q/(a*z)}]}],Product[QPochhammer[Part[{c , b/ a , z , q/ z},i],q,Infinity],{i,1,Length[{c , b/ a , z , q/ z}]}]]*QHypergeometricPFQ[{a , a*q/ c},{a*q/ b},q,c*q/(a*b*z)]+Divide[Product[QPochhammer[Part[{a , c/ b , b*z , q/(b*z)},i],q,Infinity],{i,1,Length[{a , c/ b , b*z , q/(b*z)}]}],Product[QPochhammer[Part[{c , a/ b , z , q/ z},i],q,Infinity],{i,1,Length[{c , a/ b , z , q/ z}]}]]*QHypergeometricPFQ[{b , b*q/ c},{b*q/ a},q,c*q/(a*b*z)] |
Error | Failure | - | Skipped - Because timed out |
| 17.6.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{a,b}{c/q}{q}{z}-\qgenhyperphi{2}{1}@@{a,b}{c}{q}{z} = cz\frac{(1-a)(1-b)}{(q-c)(1-c)}\qgenhyperphi{2}{1}@@{aq,bq}{cq}{q}{z}} | Error |
QHypergeometricPFQ[{a , b},{c/ q},q,z]- QHypergeometricPFQ[{a , b},{c},q,z] == c*z*Divide[(1 - a)*(1 - b),(q - c)*(1 - c)]*QHypergeometricPFQ[{a*q , b*q},{c*q},q,z] |
Error | Failure | - | Skipped - Because timed out |
| 17.6.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{aq,b}{c}{q}{z}-\qgenhyperphi{2}{1}@@{a,b}{c}{q}{z} = az\frac{1-b}{1-c}\qgenhyperphi{2}{1}@@{aq,bq}{cq}{q}{z}} | Error |
QHypergeometricPFQ[{a*q , b},{c},q,z]- QHypergeometricPFQ[{a , b},{c},q,z] == a*z*Divide[1 - b,1 - c]*QHypergeometricPFQ[{a*q , b*q},{c*q},q,z] |
Error | Failure | - | Skipped - Because timed out |
| 17.6.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{aq,b}{cq}{q}{z}-\qgenhyperphi{2}{1}@@{a,b}{c}{q}{z} = az\frac{(1-b)(1-(c/a))}{(1-c)(1-cq)}\qgenhyperphi{2}{1}@@{aq,bq}{cq^{2}}{q}{z}} | Error |
QHypergeometricPFQ[{a*q , b},{c*q},q,z]- QHypergeometricPFQ[{a , b},{c},q,z] == a*z*Divide[(1 - b)*(1 -(c/ a)),(1 - c)*(1 - c*q)]*QHypergeometricPFQ[{a*q , b*q},{c*(q)^(2)},q,z] |
Error | Failure | - | Skipped - Because timed out |
| 17.6.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{aq,b/q}{c}{q}{z}-\qgenhyperphi{2}{1}@@{a,b}{c}{q}{z} = az\frac{(1-b/(aq))}{1-c}\qgenhyperphi{2}{1}@@{aq,b}{cq}{q}{z}} | Error |
QHypergeometricPFQ[{a*q , b/ q},{c},q,z]- QHypergeometricPFQ[{a , b},{c},q,z] == a*z*Divide[1 - b/(a*q),1 - c]*QHypergeometricPFQ[{a*q , b},{c*q},q,z] |
Error | Failure | - | Skipped - Because timed out |
| 17.6.E21 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle b(1-a)\qgenhyperphi{2}{1}@@{aq,b}{c}{q}{z}-a(1-b)\qgenhyperphi{2}{1}@@{a,bq}{c}{q}{z} = (b-a)\qgenhyperphi{2}{1}@@{a,b}{c}{q}{z}} | Error |
b*(1 - a)* QHypergeometricPFQ[{a*q , b},{c},q,z]- a*(1 - b)* QHypergeometricPFQ[{a , b*q},{c},q,z] == (b - a)* QHypergeometricPFQ[{a , b},{c},q,z] |
Error | Failure | - | Skipped - Because timed out |
| 17.6.E22 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a\left(1-\frac{b}{c}\right)\qgenhyperphi{2}{1}@@{a,b/q}{c}{q}{z}-b\left(1-\frac{a}{c}\right)\qgenhyperphi{2}{1}@@{a/q,b}{c}{q}{z} = (a-b)\left(1-\frac{abz}{cq}\right)\qgenhyperphi{2}{1}@@{a,b}{c}{q}{z}} | Error |
a*(1 -Divide[b,c])* QHypergeometricPFQ[{a , b/ q},{c},q,z]- b*(1 -Divide[a,c])* QHypergeometricPFQ[{a/ q , b},{c},q,z] == (a - b)*(1 -Divide[a*b*z,c*q])* QHypergeometricPFQ[{a , b},{c},q,z] |
Error | Failure | - | Skipped - Because timed out |
| 17.6.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle q\left(1-\frac{a}{c}\right)\qgenhyperphi{2}{1}@@{a/q,b}{c}{q}{z}+(1-a)\left(1-\frac{abz}{c}\right)\qgenhyperphi{2}{1}@@{aq,b}{c}{q}{z} = \left(1+q-a-\frac{aq}{c}+\frac{a^{2}z}{c}-\frac{abz}{c}\right)\qgenhyperphi{2}{1}@@{a,b}{c}{q}{z}} | Error |
q*(1 -Divide[a,c])* QHypergeometricPFQ[{a/ q , b},{c},q,z]+(1 - a)*(1 -Divide[a*b*z,c])* QHypergeometricPFQ[{a*q , b},{c},q,z] == (1 + q - a -Divide[a*q,c]+Divide[(a)^(2)* z,c]-Divide[a*b*z,c])* QHypergeometricPFQ[{a , b},{c},q,z] |
Error | Failure | - | Skipped - Because timed out |
| 17.6.E24 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle (1-c)(q-c)(abz-c)\qgenhyperphi{2}{1}@@{a,b}{c/q}{q}{z}+z(c-a)(c-b)\qgenhyperphi{2}{1}@@{a,b}{cq}{q}{z} = (c-1)(c(q-c)+z(ca+cb-ab-abq))\qgenhyperphi{2}{1}@@{a,b}{c}{q}{z}} | Error |
(1 - c)*(q - c)*(a*b*z - c)* QHypergeometricPFQ[{a , b},{c/ q},q,z]+ z*(c - a)*(c - b)* QHypergeometricPFQ[{a , b},{c*q},q,z] == (c - 1)*(c*(q - c)+ z*(c*a + c*b - a*b - a*b*q))* QHypergeometricPFQ[{a , b},{c},q,z] |
Error | Failure | - | Skipped - Because timed out |
| 17.6.E25 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathcal{D}_{q}^{n}\qgenhyperphi{2}{1}@@{a,b}{c}{q}{zd} = \frac{\qmultiPochhammersym{a,b}{q}{n}d^{n}}{\qPochhammer{c}{q}{n}(1-q)^{n}}\qgenhyperphi{2}{1}@@{aq^{n},bq^{n}}{cq^{n}}{q}{dz}} | Error |
(Subscript[D, q])^(n)*QHypergeometricPFQ[{a , b},{c},q,z*d] == Divide[Product[QPochhammer[Part[{a , b},i],q,n],{i,1,Length[{a , b}]}]*(d)^(n),QPochhammer[c, q, n]*(1 - q)^(n)]*QHypergeometricPFQ[{a*(q)^(n), b*(q)^(n)},{c*(q)^(n)},q,d*z] |
Error | Failure | - | Skipped - Because timed out |
| 17.6.E26 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \mathcal{D}_{q}^{n}\left(\frac{\qPochhammer{z}{q}{\infty}}{\qPochhammer{abz/c}{q}{\infty}}\qgenhyperphi{2}{1}@@{a,b}{c}{q}{z}\right) = \frac{\qmultiPochhammersym{c/a,c/b}{q}{n}}{\qPochhammer{c}{q}{n}(1-q)^{n}}\left(\frac{ab}{c}\right)^{n}\frac{\qPochhammer{zq^{n}}{q}{\infty}}{\qPochhammer{abz/c}{q}{\infty}}\qgenhyperphi{2}{1}@@{a,b}{cq^{n}}{q}{zq^{n}}} | Error |
(Subscript[D, q])^(n)*(Divide[QPochhammer[z, q, Infinity],QPochhammer[a*b*z/ c, q, Infinity]]*QHypergeometricPFQ[{a , b},{c},q,z]) == Divide[Product[QPochhammer[Part[{c/ a , c/ b},i],q,n],{i,1,Length[{c/ a , c/ b}]}],QPochhammer[c, q, n]*(1 - q)^(n)]*(Divide[a*b,c])^(n)*Divide[QPochhammer[z*(q)^(n), q, Infinity],QPochhammer[a*b*z/ c, q, Infinity]]*QHypergeometricPFQ[{a , b},{c*(q)^(n)},q,z*(q)^(n)] |
Error | Failure | - | Failed [264 / 300]
{Plus[0.0, Times[Complex[0.8660254037844387, 0.49999999999999994], QHypergeometricPFQ[{-1.5, -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Power[QPochhammer[Complex[-1.299038105676658, -0.7499999999999999], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[D, q], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.0, 0.0], Times[Complex[0.5000000000000001, 0.8660254037844386], QHypergeometricPFQ[{-1.5, -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Power[QPochhammer[Complex[-1.299038105676658, -0.7499999999999999], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[D, q], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.6.E27 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z(c-abqz)\mathcal{D}_{q}^{2}\qgenhyperphi{2}{1}@@{a,b}{c}{q}{z}+\left(\frac{1-c}{1-q}+\frac{(1-a)(1-b)-(1-abq)}{1-q}z\right)\mathcal{D}_{q}\qgenhyperphi{2}{1}@@{a,b}{c}{q}{z}-\frac{(1-a)(1-b)}{(1-q)^{2}}\qgenhyperphi{2}{1}@@{a,b}{c}{q}{z} = 0} | Error |
z*(c - a*b*q*z)* (Subscript[D, q])^(2)*QHypergeometricPFQ[{a , b},{c},q,z]+(Divide[1 - c,1 - q]+Divide[(1 - a)*(1 - b)-(1 - a*b*q),1 - q]*z)* Subscript[D, q]*QHypergeometricPFQ[{a , b},{c},q,z]-Divide[(1 - a)*(1 - b),(1 - q)^(2)]*QHypergeometricPFQ[{a , b},{c},q,z] == 0 |
Error | Failure | - | Failed [300 / 300]
{Times[Complex[9.528684177437189, -1.3259618943233384], QHypergeometricPFQ[{-1.5, -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[D, q], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Times[Complex[5.290063509461103, -21.657849302036027], QHypergeometricPFQ[{-1.5, -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[D, q], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.6.E29 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{a,b}{c}{q}{z} = \left(\frac{-1}{2\pi i}\right)\frac{\qmultiPochhammersym{a,b}{q}{\infty}}{\qmultiPochhammersym{q,c}{q}{\infty}}\int_{-i\infty}^{i\infty}\frac{\qmultiPochhammersym{q^{1+\zeta},cq^{\zeta}}{q}{\infty}}{\qmultiPochhammersym{aq^{\zeta},bq^{\zeta}}{q}{\infty}}\frac{\pi(-z)^{\zeta}}{\sin@{\pi\zeta}}\diff{\zeta}} | Error |
QHypergeometricPFQ[{a , b},{c},q,z] == (Divide[- 1,2*Pi*I])*Divide[Product[QPochhammer[Part[{a , b},i],q,Infinity],{i,1,Length[{a , b}]}],Product[QPochhammer[Part[{q , c},i],q,Infinity],{i,1,Length[{q , c}]}]]*Integrate[Divide[Product[QPochhammer[Part[{(q)^(1 + \[Zeta]), c*(q)^\[Zeta]},i],q,Infinity],{i,1,Length[{(q)^(1 + \[Zeta]), c*(q)^\[Zeta]}]}],Product[QPochhammer[Part[{a*(q)^\[Zeta], b*(q)^\[Zeta]},i],q,Infinity],{i,1,Length[{a*(q)^\[Zeta], b*(q)^\[Zeta]}]}]]*Divide[Pi*(- z)^\[Zeta],Sin[Pi*\[Zeta]]], {\[Zeta], - I*Infinity, I*Infinity}, GenerateConditions->None] |
Error | Failure | - | Skipped - Because timed out |
| 17.7.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{2}@@{a,q/a}{-q,b}{q}{-b} = \frac{\qmultiPochhammersym{ab,bq/a}{q^{2}}{\infty}}{\qPochhammer{b}{q}{\infty}}} | Error |
QHypergeometricPFQ[{a , q/ a},{- q , b},q,- b] == Divide[Product[QPochhammer[Part[{a*b , b*q/ a},i],(q)^(2),Infinity],{i,1,Length[{a*b , b*q/ a}]}],QPochhammer[b, q, Infinity]] |
Error | Failure | - | Failed [96 / 120]
{Plus[QHypergeometricPFQ[{-1.5, Complex[-0.5773502691896257, -0.33333333333333326]} <- {Complex[-0.8660254037844387, -0.49999999999999994], -0.5}, Complex[0.8660254037844387, 0.49999999999999994], 0.5], Times[-1.0, Power[QPochhammer[-0.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[0.28867513459481287, 0.16666666666666663], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], QPochhammer[0.75, Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]]]], {Rule[a, -1.5], Rule[b, -0.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[a, -1.5], Rule[b, -0.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.7.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{2}@@{a^{2},b^{2}}{abq^{\frac{1}{2}},-abq^{\frac{1}{2}}}{q}{-q} = \frac{\qmultiPochhammersym{a^{2}q,b^{2}q}{q^{2}}{\infty}}{\qmultiPochhammersym{q,a^{2}b^{2}q}{q^{2}}{\infty}}} | Error |
QHypergeometricPFQ[{(a)^(2), (b)^(2)},{a*b*(q)^(Divide[1,2]), - a*b*(q)^(Divide[1,2])},q,- q] == Divide[Product[QPochhammer[Part[{(a)^(2)* q , (b)^(2)* q},i],(q)^(2),Infinity],{i,1,Length[{(a)^(2)* q , (b)^(2)* q}]}],Product[QPochhammer[Part[{q , (a)^(2)* (b)^(2)* q},i],(q)^(2),Infinity],{i,1,Length[{q , (a)^(2)* (b)^(2)* q}]}]] |
Error | Failure | - | Failed [240 / 300]
{Plus[QHypergeometricPFQ[{2.25, 2.25} <- {Complex[2.173333109150404, 0.5823428514806717], Complex[-2.173333109150404, -0.5823428514806717]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.8660254037844387, -0.49999999999999994]], Times[-1.0, Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], -1], Power[QPochhammer[Complex[1.948557158514987, 1.1249999999999998], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], 2], Power[QPochhammer[Complex[4.384253606658721, 2.5312499999999996], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], -1]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.7.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{2}@@{\ifrac{c^{2}}{b^{2}},b^{2}}{c,cq}{q^{2}}{q} = \frac{1}{2}\frac{\qmultiPochhammersym{b^{2},q}{q^{2}}{\infty}}{\qmultiPochhammersym{c,cq}{q^{2}}{\infty}}{\left(\frac{\qPochhammer{c/b}{q}{\infty}}{\qPochhammer{b}{q}{\infty}}+\frac{\qPochhammer{-c/b}{q}{\infty}}{\qPochhammer{-b}{q}{\infty}}\right)}} | Error |
QHypergeometricPFQ[{Divide[(c)^(2),(b)^(2)], (b)^(2)},{c , c*q},(q)^(2),q] == Divide[1,2]*Divide[Product[QPochhammer[Part[{(b)^(2), q},i],(q)^(2),Infinity],{i,1,Length[{(b)^(2), q}]}],Product[QPochhammer[Part[{c , c*q},i],(q)^(2),Infinity],{i,1,Length[{c , c*q}]}]]*(Divide[QPochhammer[c/ b, q, Infinity],QPochhammer[b, q, Infinity]]+Divide[QPochhammer[- c/ b, q, Infinity],QPochhammer[- b, q, Infinity]]) |
Error | Failure | - | Failed [260 / 300]
{Plus[QHypergeometricPFQ[{1.0, 2.25} <- {-1.5, Complex[-1.299038105676658, -0.7499999999999999]}, Complex[0.5000000000000001, 0.8660254037844386], Complex[0.8660254037844387, 0.49999999999999994]], Times[-0.5, Power[QPochhammer[-1.5, Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], -1], Power[QPochhammer[Complex[-1.299038105676658, -0.7499999999999999], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], -1], QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], Plus[0.0, Times[QPochhammer[-1.0, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[1.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]]], QPochhammer[2.25, Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.7.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{3}{2}@@{a,b,q^{-n}}{c,abq^{1-n}/c}{q}{q} = \frac{\qmultiPochhammersym{c/a,c/b}{q}{n}}{\qmultiPochhammersym{c,c/(ab)}{q}{n}}} | Error |
QHypergeometricPFQ[{a , b , (q)^(- n)},{c , a*b*(q)^(1 - n)/ c},q,q] == Divide[Product[QPochhammer[Part[{c/ a , c/ b},i],q,n],{i,1,Length[{c/ a , c/ b}]}],Product[QPochhammer[Part[{c , c/(a*b)},i],q,n],{i,1,Length[{c , c/(a*b)}]}]] |
Error | Failure | - | Failed [196 / 300]
{Plus[0.0, QHypergeometricPFQ[{-1.5, -1.5, Complex[0.8660254037844387, -0.49999999999999994]} <- {-1.5, -1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, -1.5, Complex[0.5000000000000001, -0.8660254037844386]} <- {-1.5, Complex[-1.299038105676658, 0.7499999999999999]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.7.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{3}{2}@@{a,b,c}{e,f}{q}{q}+\frac{\qmultiPochhammersym{q/e,a,b,c,qf/e}{q}{\infty}}{\qmultiPochhammersym{e/q,aq/e,bq/e,cq/e,f}{q}{\infty}}\*\qgenhyperphi{3}{2}@@{aq/e,bq/e,cq/e}{q^{2}/e,qf/e}{q}{q} = \frac{\qmultiPochhammersym{q/e,f/a,f/b,f/c}{q}{\infty}}{\qmultiPochhammersym{aq/e,bq/e,cq/e,f}{q}{\infty}}} | Error |
QHypergeometricPFQ[{a , b , c},{e , f},q,q]+Divide[Product[QPochhammer[Part[{q/ e , a , b , c , q*f/ e},i],q,Infinity],{i,1,Length[{q/ e , a , b , c , q*f/ e}]}],Product[QPochhammer[Part[{e/ q , a*q/ e , b*q/ e , c*q/ e , f},i],q,Infinity],{i,1,Length[{e/ q , a*q/ e , b*q/ e , c*q/ e , f}]}]]* QHypergeometricPFQ[{a*q/ e , b*q/ e , c*q/ e},{(q)^(2)/ e , q*f/ e},q,q] == Divide[Product[QPochhammer[Part[{q/ e , f/ a , f/ b , f/ c},i],q,Infinity],{i,1,Length[{q/ e , f/ a , f/ b , f/ c}]}],Product[QPochhammer[Part[{a*q/ e , b*q/ e , c*q/ e , f},i],q,Infinity],{i,1,Length[{a*q/ e , b*q/ e , c*q/ e , f}]}]] |
Error | Failure | - | Failed [300 / 300]
{Plus[0.0, QHypergeometricPFQ[{-1.5, -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[QHypergeometricPFQ[{Complex[-1.5, 0.0], Complex[-1.5, 0.0], Complex[-1.5, 0.0]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Power[QPochhammer[-1.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], 3], Power[QPochhammer[Complex[-1.5, 0.0], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -3]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.7.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{3}{2}@@{q^{-2n},b,c}{q^{1-2n}/b,q^{1-2n}/c}{q}{\frac{q^{2-n}}{bc}} = \frac{\qmultiPochhammersym{b,c}{q}{n}\qmultiPochhammersym{q,bc}{q}{2n}}{\qmultiPochhammersym{q,bc}{q}{n}\qmultiPochhammersym{b,c}{q}{2n}}} | Error |
QHypergeometricPFQ[{(q)^(- 2*n), b , c},{(q)^(1 - 2*n)/ b , (q)^(1 - 2*n)/ c},q,Divide[(q)^(2 - n),b*c]] == Divide[Product[QPochhammer[Part[{b , c},i],q,n],{i,1,Length[{b , c}]}]*Product[QPochhammer[Part[{q , b*c},i],q,2*n],{i,1,Length[{q , b*c}]}],Product[QPochhammer[Part[{q , b*c},i],q,n],{i,1,Length[{q , b*c}]}]*Product[QPochhammer[Part[{b , c},i],q,2*n],{i,1,Length[{b , c}]}]] |
Error | Failure | - | Skipped - Because timed out |
| 17.7.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{4}{3}@@{a,-qa^{\frac{1}{2}},b,c}{-a^{\frac{1}{2}},aq/b,aq/c}{q}{\frac{qa^{\frac{1}{2}}}{bc}} = \frac{\qmultiPochhammersym{aq,qa^{\frac{1}{2}}/b,qa^{\frac{1}{2}}/c,aq/(bc)}{q}{\infty}}{\qmultiPochhammersym{aq/b,aq/c,qa^{\frac{1}{2}},qa^{\frac{1}{2}}/(bc)}{q}{\infty}}} | Error |
QHypergeometricPFQ[{a , - q*(a)^(Divide[1,2]), b , c},{- (a)^(Divide[1,2]), a*q/ b , a*q/ c},q,Divide[q*(a)^(Divide[1,2]),b*c]] == Divide[Product[QPochhammer[Part[{a*q , q*(a)^(Divide[1,2])/ b , q*(a)^(Divide[1,2])/ c , a*q/(b*c)},i],q,Infinity],{i,1,Length[{a*q , q*(a)^(Divide[1,2])/ b , q*(a)^(Divide[1,2])/ c , a*q/(b*c)}]}],Product[QPochhammer[Part[{a*q/ b , a*q/ c , q*(a)^(Divide[1,2]), q*(a)^(Divide[1,2])/(b*c)},i],q,Infinity],{i,1,Length[{a*q/ b , a*q/ c , q*(a)^(Divide[1,2]), q*(a)^(Divide[1,2])/(b*c)}]}]] |
Error | Failure | - | Failed [248 / 300]
{Plus[QHypergeometricPFQ[{-1.5, Complex[0.6123724356957944, -1.0606601717798212], -1.5, -1.5} <- {Complex[0.0, -1.224744871391589], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.27216552697590857, 0.4714045207910316]], Times[-1.0, QPochhammer[Complex[-1.299038105676658, -0.7499999999999999], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[-0.6123724356957944, 1.0606601717798212], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[-0.5773502691896257, -0.33333333333333326], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[-0.27216552697590857, 0.4714045207910316], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], Power[QPochhammer[Complex[0.4082482904638629, -0.7071067811865475], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], 2], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -2]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.7.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{8}{7}@@{\lambda,q\lambda^{\frac{1}{2}},-q\lambda^{\frac{1}{2}},a,b,c,-c,\lambda q/c^{2}}{\lambda^{\frac{1}{2}},-\lambda^{\frac{1}{2}},\lambda q/a,\lambda q/b,\lambda q/c,-\lambda q/c,c^{2}}{q}{-\frac{\lambda q}{ab}} = \frac{\qmultiPochhammersym{\lambda q,c^{2}/\lambda}{q}{\infty}\qmultiPochhammersym{aq,bq,c^{2}q/a,c^{2}q/b}{q^{2}}{\infty}}{\qmultiPochhammersym{\lambda q/a,\lambda q/b}{q}{\infty}\qmultiPochhammersym{q,abq,c^{2}q,c^{2}q/(ab)}{q^{2}}{\infty}}} | Error |
QHypergeometricPFQ[{\[Lambda], q*\[Lambda]^(Divide[1,2]), - q*\[Lambda]^(Divide[1,2]), a , b , c , - c , \[Lambda]*q/ (c)^(2)},{\[Lambda]^(Divide[1,2]), - \[Lambda]^(Divide[1,2]), \[Lambda]*q/ a , \[Lambda]*q/ b , \[Lambda]*q/ c , - \[Lambda]*q/ c , (c)^(2)},q,-Divide[\[Lambda]*q,a*b]] == Divide[Product[QPochhammer[Part[{\[Lambda]*q , (c)^(2)/ \[Lambda]},i],q,Infinity],{i,1,Length[{\[Lambda]*q , (c)^(2)/ \[Lambda]}]}]*Product[QPochhammer[Part[{a*q , b*q , (c)^(2)* q/ a , (c)^(2)* q/ b},i],(q)^(2),Infinity],{i,1,Length[{a*q , b*q , (c)^(2)* q/ a , (c)^(2)* q/ b}]}],Product[QPochhammer[Part[{\[Lambda]*q/ a , \[Lambda]*q/ b},i],q,Infinity],{i,1,Length[{\[Lambda]*q/ a , \[Lambda]*q/ b}]}]*Product[QPochhammer[Part[{q , a*b*q , (c)^(2)* q , (c)^(2)* q/(a*b)},i],(q)^(2),Infinity],{i,1,Length[{q , a*b*q , (c)^(2)* q , (c)^(2)* q/(a*b)}]}]] |
Error | Failure | - | Skipped - Because timed out |
| 17.7.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{4}{3}@@{q^{-n},q^{n+1},c,-c}{e,c^{2}q/e,-q}{q}{q} = \frac{\qmultiPochhammersym{eq^{-n},eq^{n+1},c^{2}q^{1-n}/e,c^{2}q^{n+2}/e}{q^{2}}{\infty}}{\qmultiPochhammersym{e,c^{2}q/e}{q}{\infty}}} | Error |
QHypergeometricPFQ[{(q)^(- n), (q)^(n + 1), c , - c},{e , (c)^(2)* q/ e , - q},q,q] == Divide[Product[QPochhammer[Part[{e*(q)^(- n), e*(q)^(n + 1), (c)^(2)* (q)^(1 - n)/ e , (c)^(2)* (q)^(n + 2)/ e},i],(q)^(2),Infinity],{i,1,Length[{e*(q)^(- n), e*(q)^(n + 1), (c)^(2)* (q)^(1 - n)/ e , (c)^(2)* (q)^(n + 2)/ e}]}],Product[QPochhammer[Part[{e , (c)^(2)* q/ e},i],q,Infinity],{i,1,Length[{e , (c)^(2)* q/ e}]}]] |
Error | Failure | - | Failed [296 / 300]
{Plus[0.0, QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], Complex[0.5000000000000001, 0.8660254037844386], -1.5, 1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[2.25, 0.0], Complex[-0.8660254037844387, -0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[c, -1.5], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], Complex[0.0, 1.0], -1.5, 1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[2.25, 0.0], Complex[-0.8660254037844387, -0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[-1.0, QPochhammer[Complex[-0.49999999999999994, 0.8660254037844387], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], QPochhammer[Complex[3.3306690738754696*^-16, 2.25], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], QPochhammer[Complex[0.8660254037844387, -0.49999999999999994], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[1.1250000000000004, -1.9485571585149868], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], Power[QPochhammer[Complex[2.25, 0.0], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]]], {Rule[c, -1.5], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.7.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{4}{3}@@{a,aq,b^{2}q^{2n},q^{-2n}}{b,bq,a^{2}q^{2}}{q^{2}}{q^{2}} = \frac{a^{n}\qmultiPochhammersym{-q,b/a}{q}{n}}{\qmultiPochhammersym{-aq,b}{q}{n}}} | Error |
QHypergeometricPFQ[{a , a*q , (b)^(2)* (q)^(2*n), (q)^(- 2*n)},{b , b*q , (a)^(2)* (q)^(2)},(q)^(2),(q)^(2)] == Divide[(a)^(n)* Product[QPochhammer[Part[{- q , b/ a},i],q,n],{i,1,Length[{- q , b/ a}]}],Product[QPochhammer[Part[{- a*q , b},i],q,n],{i,1,Length[{- a*q , b}]}]] |
Error | Failure | - | Failed [246 / 300]
{Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[-1.299038105676658, -0.7499999999999999], Complex[1.1250000000000002, 1.9485571585149868], Complex[0.5000000000000001, -0.8660254037844386]} <- {-1.5, Complex[-1.299038105676658, -0.7499999999999999], Complex[1.1250000000000002, 1.9485571585149868]}, Complex[0.5000000000000001, 0.8660254037844386], Complex[0.5000000000000001, 0.8660254037844386]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[-1.299038105676658, -0.7499999999999999], Complex[-1.1249999999999996, 1.948557158514987], Complex[-0.4999999999999998, -0.8660254037844387]} <- {-1.5, Complex[-1.299038105676658, -0.7499999999999999], Complex[1.1250000000000002, 1.9485571585149868]}, Complex[0.5000000000000001, 0.8660254037844386], Complex[0.5000000000000001, 0.8660254037844386]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.7.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{4}{3}@@{a,aq,b^{2}q^{2n-2},q^{-2n}}{b,bq,a^{2}}{q^{2}}{q^{2}} = \frac{a^{n}\qmultiPochhammersym{-q,b/a}{q}{n}(1-bq^{n-1})}{\qmultiPochhammersym{-a,b}{q}{n}(1-bq^{2n-1})}} | Error |
QHypergeometricPFQ[{a , a*q , (b)^(2)* (q)^(2*n - 2), (q)^(- 2*n)},{b , b*q , (a)^(2)},(q)^(2),(q)^(2)] == Divide[(a)^(n)* Product[QPochhammer[Part[{- q , b/ a},i],q,n],{i,1,Length[{- q , b/ a}]}]*(1 - b*(q)^(n - 1)),Product[QPochhammer[Part[{- a , b},i],q,n],{i,1,Length[{- a , b}]}]*(1 - b*(q)^(2*n - 1))] |
Error | Failure | - | Failed [210 / 300]
{Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[-1.299038105676658, -0.7499999999999999], 2.25, Complex[0.5000000000000001, -0.8660254037844386]} <- {-1.5, Complex[-1.299038105676658, -0.7499999999999999], 2.25}, Complex[0.5000000000000001, 0.8660254037844386], Complex[0.5000000000000001, 0.8660254037844386]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[-1.299038105676658, -0.7499999999999999], Complex[1.1250000000000002, 1.9485571585149868], Complex[-0.4999999999999998, -0.8660254037844387]} <- {-1.5, Complex[-1.299038105676658, -0.7499999999999999], 2.25}, Complex[0.5000000000000001, 0.8660254037844386], Complex[0.5000000000000001, 0.8660254037844386]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.7.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{6}{5}@@{a,qa^{\frac{1}{2}},-qa^{\frac{1}{2}},b,c,q^{-n}}{a^{\frac{1}{2}},-a^{\frac{1}{2}},aq/b,aq/c,aq^{n+1}}{q}{\frac{aq^{n+1}}{bc}} = \frac{\qmultiPochhammersym{aq,aq/(bc)}{q}{n}}{\qmultiPochhammersym{aq/b,aq/c}{q}{n}}} | Error |
QHypergeometricPFQ[{a , q*(a)^(Divide[1,2]), - q*(a)^(Divide[1,2]), b , c , (q)^(- n)},{(a)^(Divide[1,2]), - (a)^(Divide[1,2]), a*q/ b , a*q/ c , a*(q)^(n + 1)},q,Divide[a*(q)^(n + 1),b*c]] == Divide[Product[QPochhammer[Part[{a*q , a*q/(b*c)},i],q,n],{i,1,Length[{a*q , a*q/(b*c)}]}],Product[QPochhammer[Part[{a*q/ b , a*q/ c},i],q,n],{i,1,Length[{a*q/ b , a*q/ c}]}]] |
Error | Failure | - | Failed [240 / 300]
{Plus[Complex[14.55021169820366, 2.220446049250313*^-16], QHypergeometricPFQ[{-1.5, Complex[-0.6123724356957944, 1.0606601717798212], Complex[0.6123724356957944, -1.0606601717798212], -1.5, -1.5, Complex[0.8660254037844387, -0.49999999999999994]} <- {Complex[0.0, 1.224744871391589], Complex[0.0, -1.224744871391589], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.7500000000000002, -1.299038105676658]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.33333333333333337, -0.5773502691896257]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[-46.07567037764495, -8.881784197001252*^-15], QHypergeometricPFQ[{-1.5, Complex[-0.6123724356957944, 1.0606601717798212], Complex[0.6123724356957944, -1.0606601717798212], -1.5, -1.5, Complex[0.5000000000000001, -0.8660254037844386]} <- {Complex[0.0, 1.224744871391589], Complex[0.0, -1.224744871391589], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.0, -1.5]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.0, -0.6666666666666666]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.7.E20 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{k=0}^{n}\frac{1-ap^{k}q^{k}}{1-a}\frac{\qPochhammer{a}{p}{k}\qPochhammer{c}{q}{k}}{\qPochhammer{q}{q}{k}\qPochhammer{ap/c}{p}{k}}c^{-k} = \frac{\qPochhammer{ap}{p}{n}\qPochhammer{cq}{q}{n}}{\qPochhammer{q}{q}{n}\qPochhammer{ap/c}{p}{n}}c^{-n}} | sum((1 - a*(p)^(k)* (q)^(k))/(1 - a)*(QPochhammer(a, p, k)*QPochhammer(c, q, k))/(QPochhammer(q, q, k)*QPochhammer(a*p/ c, p, k))*(c)^(- k), k = 0..n) = (QPochhammer(a*p, p, n)*QPochhammer(c*q, q, n))/(QPochhammer(q, q, n)*QPochhammer(a*p/ c, p, n))*(c)^(- n) |
Sum[Divide[1 - a*(p)^(k)* (q)^(k),1 - a]*Divide[QPochhammer[a, p, k]*QPochhammer[c, q, k],QPochhammer[q, q, k]*QPochhammer[a*p/ c, p, k]]*(c)^(- k), {k, 0, n}, GenerateConditions->None] == Divide[QPochhammer[a*p, p, n]*QPochhammer[c*q, q, n],QPochhammer[q, q, n]*QPochhammer[a*p/ c, p, n]]*(c)^(- n) |
Failure | Error | Error | Skipped - Because timed out |
| 17.9.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{a,b}{c}{q}{z} = \frac{\qPochhammer{za}{q}{\infty}}{\qPochhammer{z}{q}{\infty}}\qgenhyperphi{2}{2}@@{a,c/b}{c,az}{q}{bz}} | Error |
QHypergeometricPFQ[{a , b},{c},q,z] == Divide[QPochhammer[z*a, q, Infinity],QPochhammer[z, q, Infinity]]*QHypergeometricPFQ[{a , c/ b},{c , a*z},q,b*z] |
Error | Failure | - | Skipped - Because timed out |
| 17.9.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{q^{-n},b}{c}{q}{z} = \frac{\qPochhammer{c/b}{q}{n}}{\qPochhammer{c}{q}{n}}b^{n}\qgenhyperphi{3}{1}@@{q^{-n},b,q/z}{bq^{1-n}/c}{q}{z/c}} | Error |
QHypergeometricPFQ[{(q)^(- n), b},{c},q,z] == Divide[QPochhammer[c/ b, q, n],QPochhammer[c, q, n]]*(b)^(n)* QHypergeometricPFQ[{(q)^(- n), b , q/ z},{b*(q)^(1 - n)/ c},q,z/ c] |
Error | Failure | - | Failed [290 / 300]
{Plus[0.0, QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.9.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{a,b}{c}{q}{z} = \frac{\qPochhammer{abz/c}{q}{\infty}}{\qPochhammer{bz/c}{q}{\infty}}\qgenhyperphi{3}{2}@@{a,c/b,0}{c,cq/(bz)}{q}{q}+\frac{\qmultiPochhammersym{a,bz,c/b}{q}{\infty}}{\qmultiPochhammersym{c,z,c/(bz)}{q}{\infty}}\qgenhyperphi{3}{2}@@{z,abz/c,0}{bz,bzq/c}{q}{q}} | Error |
QHypergeometricPFQ[{a , b},{c},q,z] == Divide[QPochhammer[a*b*z/ c, q, Infinity],QPochhammer[b*z/ c, q, Infinity]]*QHypergeometricPFQ[{a , c/ b , 0},{c , c*q/(b*z)},q,q]+Divide[Product[QPochhammer[Part[{a , b*z , c/ b},i],q,Infinity],{i,1,Length[{a , b*z , c/ b}]}],Product[QPochhammer[Part[{c , z , c/(b*z)},i],q,Infinity],{i,1,Length[{c , z , c/(b*z)}]}]]*QHypergeometricPFQ[{z , a*b*z/ c , 0},{b*z , b*z*q/ c},q,q] |
Error | Failure | - | Skipped - Because timed out |
| 17.9.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{q^{-n},b}{c}{q}{z} = \frac{\qPochhammer{c/b}{q}{n}}{\qPochhammer{c}{q}{n}}\left(\frac{bz}{q}\right)^{n}\qgenhyperphi{3}{2}@@{q^{-n},q/z,q^{1-n}/c}{bq^{1-n}/c,0}{q}{q}} | Error |
QHypergeometricPFQ[{(q)^(- n), b},{c},q,z] == Divide[QPochhammer[c/ b, q, n],QPochhammer[c, q, n]]*(Divide[b*z,q])^(n)* QHypergeometricPFQ[{(q)^(- n), q/ z , (q)^(1 - n)/ c},{b*(q)^(1 - n)/ c , 0},q,q] |
Error | Failure | - | Failed [294 / 300]
{Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.9.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{2}{1}@@{q^{-n},b}{c}{q}{z} = \frac{\qPochhammer{c/b}{q}{n}}{\qPochhammer{c}{q}{n}}\qgenhyperphi{3}{2}@@{q^{-n},b,bzq^{-n}/c}{bq^{1-n}/c,0}{q}{q}} | Error |
QHypergeometricPFQ[{(q)^(- n), b},{c},q,z] == Divide[QPochhammer[c/ b, q, n],QPochhammer[c, q, n]]*QHypergeometricPFQ[{(q)^(- n), b , b*z*(q)^(- n)/ c},{b*(q)^(1 - n)/ c , 0},q,q] |
Error | Failure | - | Failed [294 / 300]
{Plus[0.0, QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.9.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{3}{2}@@{a,b,c}{d,e}{q}{de/(abc)} = \frac{\qmultiPochhammersym{e/a,de/(bc)}{q}{\infty}}{\qmultiPochhammersym{e,de/(abc)}{q}{\infty}}\qgenhyperphi{3}{2}@@{a,d/b,d/c}{d,de/(bc)}{q}{e/a}} | Error |
QHypergeometricPFQ[{a , b , c},{d , e},q,d*e/(a*b*c)] == Divide[Product[QPochhammer[Part[{e/ a , d*e/(b*c)},i],q,Infinity],{i,1,Length[{e/ a , d*e/(b*c)}]}],Product[QPochhammer[Part[{e , d*e/(a*b*c)},i],q,Infinity],{i,1,Length[{e , d*e/(a*b*c)}]}]]*QHypergeometricPFQ[{a , d/ b , d/ c},{d , d*e/(b*c)},q,e/ a] |
Error | Failure | - | Failed [264 / 300]
{Plus[QHypergeometricPFQ[{-1.5, -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.14814814814814822, -0.25660011963983365]], Times[-1.0, QHypergeometricPFQ[{-1.5, Complex[-0.5773502691896257, -0.33333333333333326], Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.2222222222222223, 0.38490017945975047]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.5773502691896257, -0.33333333333333326]], QPochhammer[Complex[-0.5773502691896257, -0.33333333333333326], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[-0.14814814814814822, -0.25660011963983365], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[0.2222222222222223, 0.38490017945975047], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.9.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{3}{2}@@{a,b,c}{d,e}{q}{de/(abc)} = \frac{\qmultiPochhammersym{b,de/(ab),de/(bc)}{q}{\infty}}{\qmultiPochhammersym{d,e,de/(abc)}{q}{\infty}}\*\qgenhyperphi{3}{2}@@{d/b,e/b,de/(abc)}{de/(ab),de/(bc)}{q}{b}} | Error |
QHypergeometricPFQ[{a , b , c},{d , e},q,d*e/(a*b*c)] == Divide[Product[QPochhammer[Part[{b , d*e/(a*b), d*e/(b*c)},i],q,Infinity],{i,1,Length[{b , d*e/(a*b), d*e/(b*c)}]}],Product[QPochhammer[Part[{d , e , d*e/(a*b*c)},i],q,Infinity],{i,1,Length[{d , e , d*e/(a*b*c)}]}]]* QHypergeometricPFQ[{d/ b , e/ b , d*e/(a*b*c)},{d*e/(a*b), d*e/(b*c)},q,b] |
Error | Failure | - | Failed [300 / 300]
{Plus[QHypergeometricPFQ[{-1.5, -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.14814814814814822, -0.25660011963983365]], Times[-1.0, QHypergeometricPFQ[{Complex[-0.5773502691896257, -0.33333333333333326], Complex[-0.5773502691896257, -0.33333333333333326], Complex[-0.14814814814814822, -0.25660011963983365]}, {Complex[0.2222222222222223, 0.38490017945975047], Complex[0.2222222222222223, 0.38490017945975047]}, Complex[0.8660254037844387, 0.49999999999999994], -1.5], QPochhammer[-1.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[-0.14814814814814822, -0.25660011963983365], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], Power[QPochhammer[Complex[0.2222222222222223, 0.38490017945975047], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], 2], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -2]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.9.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{3}{2}@@{q^{-n},b,c}{d,e}{q}{q} = \frac{\qPochhammer{de/(bc)}{q}{n}}{\qPochhammer{e}{q}{n}}\left(\frac{bc}{d}\right)^{n}\qgenhyperphi{3}{2}@@{q^{-n},d/b,d/c}{d,de/(bc)}{q}{q}} | Error |
QHypergeometricPFQ[{(q)^(- n), b , c},{d , e},q,q] == Divide[QPochhammer[d*e/(b*c), q, n],QPochhammer[e, q, n]]*(Divide[b*c,d])^(n)* QHypergeometricPFQ[{(q)^(- n), d/ b , d/ c},{d , d*e/(b*c)},q,q] |
Error | Failure | - | Failed [188 / 300]
{Plus[QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[Complex[-3.573557158514987, -1.2075317547305489], QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], Complex[-0.5773502691896257, -0.33333333333333326], Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.2222222222222223, 0.38490017945975047]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[Complex[-8.437338913245533, -3.8821710443592976], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], Complex[-0.5773502691896257, -0.33333333333333326], Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.2222222222222223, 0.38490017945975047]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.9.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{3}{2}@@{q^{-n},b,c}{d,e}{q}{q} = \frac{\qPochhammer{e/c}{q}{n}}{\qPochhammer{e}{q}{n}}c^{n}\qgenhyperphi{3}{2}@@{q^{-n},c,d/b}{d,cq^{1-n}/e}{q}{\frac{bq}{e}}} | Error |
QHypergeometricPFQ[{(q)^(- n), b , c},{d , e},q,q] == Divide[QPochhammer[e/ c, q, n],QPochhammer[e, q, n]]*(c)^(n)* QHypergeometricPFQ[{(q)^(- n), c , d/ b},{d , c*(q)^(1 - n)/ e},q,Divide[b*q,e]] |
Error | Failure | - | Failed [228 / 300]
{Plus[QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[Complex[0.2499999999999999, 4.665063509461097], QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[-1.299038105676658, 0.7499999999999999]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-1.5, 0.0]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[Complex[10.037658773652746, -1.7075317547305477], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5, Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.7500000000000001, 1.2990381056766578]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-1.5, 0.0]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.9.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{3}{2}@@{q^{-n},b,c}{d,e}{q}{\frac{deq^{n}}{bc}} = \frac{\qPochhammer{e/c}{q}{n}}{\qPochhammer{e}{q}{n}}\qgenhyperphi{3}{2}@@{q^{-n},c,d/b}{d,cq^{1-n}/e}{q}{q}} | Error |
QHypergeometricPFQ[{(q)^(- n), b , c},{d , e},q,Divide[d*e*(q)^(n),b*c]] == Divide[QPochhammer[e/ c, q, n],QPochhammer[e, q, n]]*QHypergeometricPFQ[{(q)^(- n), c , d/ b},{d , c*(q)^(1 - n)/ e},q,q] |
Error | Failure | - | Failed [198 / 300]
{Plus[QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[1.1102230246251565*^-16, 0.4444444444444444]], Times[Complex[-0.16666666666666663, -3.1100423396407315], QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[-1.299038105676658, 0.7499999999999999]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.2222222222222221, 0.38490017945975064]], Times[Complex[4.461181677178999, -0.7589030021024659], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5, Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.7500000000000001, 1.2990381056766578]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.9.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{3}{2}@@{q^{-n},b,c}{d,e}{q}{q} = \frac{\qmultiPochhammersym{e/c,d/c}{q}{n}}{\qmultiPochhammersym{e,d}{q}{n}}c^{n}\qgenhyperphi{3}{2}@@{q^{-n},c,\ifrac{cbq^{1-n}}{(de)}}{\ifrac{cq^{1-n}}{e},\ifrac{cq^{1-n}}{d}}{q}{q}} | Error |
QHypergeometricPFQ[{(q)^(- n), b , c},{d , e},q,q] == Divide[Product[QPochhammer[Part[{e/ c , d/ c},i],q,n],{i,1,Length[{e/ c , d/ c}]}],Product[QPochhammer[Part[{e , d},i],q,n],{i,1,Length[{e , d}]}]]*(c)^(n)* QHypergeometricPFQ[{(q)^(- n), c ,Divide[c*b*(q)^(1 - n),d*e]},{Divide[c*(q)^(1 - n),e],Divide[c*(q)^(1 - n),d]},q,q] |
Error | Failure | - | Failed [210 / 300]
{Plus[QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[Complex[-14.466878364870325, 1.5550211698203658], QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, Complex[1.1250000000000004, -1.9485571585149868]}, {Complex[-1.299038105676658, 0.7499999999999999], Complex[-1.299038105676658, 0.7499999999999999]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[Complex[-43.48396842794434, 15.235218754810454], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5, Complex[6.661338147750939*^-16, -2.25]}, {Complex[-0.7500000000000001, 1.2990381056766578], Complex[-0.7500000000000001, 1.2990381056766578]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.9.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{3}{2}@@{a,b,c}{d,e}{q}{\frac{de}{abc}} = \frac{\qmultiPochhammersym{e/b,e/c,cq/a,q/d}{q}{\infty}}{\qmultiPochhammersym{e,cq/d,q/a,e/(bc)}{q}{\infty}}\qgenhyperphi{3}{2}@@{c,d/a,cq/e}{cq/a,bcq/e}{q}{\frac{bq}{d}}-\frac{\qmultiPochhammersym{q/d,eq/d,b,c,d/a,de/(bcq),bcq^{2}/(de)}{q}{\infty}}{\qmultiPochhammersym{d/q,e,bq/d,cq/d,q/a,e/(bc),bcq/e}{q}{\infty}}\qgenhyperphi{3}{2}@@{aq/d,bq/d,cq/d}{q^{2}/d,eq/d}{q}{\frac{de}{abc}}} | Error |
QHypergeometricPFQ[{a , b , c},{d , e},q,Divide[d*e,a*b*c]] == Divide[Product[QPochhammer[Part[{e/ b , e/ c , c*q/ a , q/ d},i],q,Infinity],{i,1,Length[{e/ b , e/ c , c*q/ a , q/ d}]}],Product[QPochhammer[Part[{e , c*q/ d , q/ a , e/(b*c)},i],q,Infinity],{i,1,Length[{e , c*q/ d , q/ a , e/(b*c)}]}]]*QHypergeometricPFQ[{c , d/ a , c*q/ e},{c*q/ a , b*c*q/ e},q,Divide[b*q,d]]-Divide[Product[QPochhammer[Part[{q/ d , e*q/ d , b , c , d/ a , d*e/(b*c*q), b*c*(q)^(2)/(d*e)},i],q,Infinity],{i,1,Length[{q/ d , e*q/ d , b , c , d/ a , d*e/(b*c*q), b*c*(q)^(2)/(d*e)}]}],Product[QPochhammer[Part[{d/ q , e , b*q/ d , c*q/ d , q/ a , e/(b*c), b*c*q/ e},i],q,Infinity],{i,1,Length[{d/ q , e , b*q/ d , c*q/ d , q/ a , e/(b*c), b*c*q/ e}]}]]*QHypergeometricPFQ[{a*q/ d , b*q/ d , c*q/ d},{(q)^(2)/ d , e*q/ d},q,Divide[d*e,a*b*c]] |
Error | Failure | - | Failed [246 / 300]
{Plus[0.0, QHypergeometricPFQ[{-1.5, -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.14814814814814822, -0.25660011963983365]], Times[QHypergeometricPFQ[{Complex[-1.5, 0.0], Complex[-1.5, 0.0], Complex[-1.5, 0.0]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.14814814814814822, -0.25660011963983365]], Power[QPochhammer[-1.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], 2], Power[QPochhammer[Complex[-1.5, 0.0], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -2], Power[QPochhammer[Complex[2.25, 0.0], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[2.25, 2.220446049250313*^-16], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.9.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{3}{2}@@{a,b,c}{d,e}{q}{\frac{de}{abc}} = \frac{\qmultiPochhammersym{e/b,e/c}{q}{\infty}}{\qmultiPochhammersym{e,e/(bc)}{q}{\infty}}\qgenhyperphi{3}{2}@@{d/a,b,c}{d,bcq/e}{q}{q}+\frac{\qmultiPochhammersym{d/a,b,c,de/(bc)}{q}{\infty}}{\qmultiPochhammersym{d,e,bc/e,de/(abc)}{q}{\infty}}\qgenhyperphi{3}{2}@@{e/b,e/c,de/(abc)}{de/(bc),eq/(bc)}{q}{q}} | Error |
QHypergeometricPFQ[{a , b , c},{d , e},q,Divide[d*e,a*b*c]] == Divide[Product[QPochhammer[Part[{e/ b , e/ c},i],q,Infinity],{i,1,Length[{e/ b , e/ c}]}],Product[QPochhammer[Part[{e , e/(b*c)},i],q,Infinity],{i,1,Length[{e , e/(b*c)}]}]]*QHypergeometricPFQ[{d/ a , b , c},{d , b*c*q/ e},q,q]+Divide[Product[QPochhammer[Part[{d/ a , b , c , d*e/(b*c)},i],q,Infinity],{i,1,Length[{d/ a , b , c , d*e/(b*c)}]}],Product[QPochhammer[Part[{d , e , b*c/ e , d*e/(a*b*c)},i],q,Infinity],{i,1,Length[{d , e , b*c/ e , d*e/(a*b*c)}]}]]*QHypergeometricPFQ[{e/ b , e/ c , d*e/(a*b*c)},{d*e/(b*c), e*q/(b*c)},q,q] |
Error | Failure | - | Failed [246 / 300]
{Plus[QHypergeometricPFQ[{-1.5, -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.14814814814814822, -0.25660011963983365]], Times[-1.0, QHypergeometricPFQ[{Complex[-0.5773502691896257, -0.33333333333333326], -1.5, -1.5}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[2.25, 0.0]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Power[QPochhammer[Complex[-0.5773502691896257, -0.33333333333333326], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], 2], Power[QPochhammer[Complex[0.3849001794597505, 0.22222222222222218], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]], Times[-1.0, QHypergeometricPFQ[{Complex[-0.5773502691896257, -0.33333333333333326], Complex[-0.5773502691896257, -0.33333333333333326], Complex[-0.14814814814814822, -0.25660011963983365]}, {Complex[0.2222222222222223, 0.38490017945975047], Complex[0.2222222222222223, 0.38490017945975047]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Power[QPochhammer[-1.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], 2], QPochhammer[Complex[-0.5773502691896257, -0.33333333333333326], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[-0.14814814814814822, -0.25660011963983365], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[0.2222222222222223, 0.38490017945975047], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -2], Power[QPochhammer[Complex[1.948557158514987, -1.1249999999999998], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.9.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{4}{3}@@{q^{-n},a,b,c}{d,e,f}{q}{q} = \frac{\qmultiPochhammersym{e/a,f/a}{q}{n}}{\qmultiPochhammersym{e,f}{q}{n}}a^{n}\qgenhyperphi{4}{3}@@{q^{-n},a,d/b,d/c}{d,aq^{1-n}/e,aq^{1-n}/f}{q}{q}} | Error |
QHypergeometricPFQ[{(q)^(- n), a , b , c},{d , e , f},q,q] == Divide[Product[QPochhammer[Part[{e/ a , f/ a},i],q,n],{i,1,Length[{e/ a , f/ a}]}],Product[QPochhammer[Part[{e , f},i],q,n],{i,1,Length[{e , f}]}]]*(a)^(n)* QHypergeometricPFQ[{(q)^(- n), a , d/ b , d/ c},{d , a*(q)^(1 - n)/ e , a*(q)^(1 - n)/ f},q,q] |
Error | Failure | - | Skipped - Because timed out |
| 17.9.E14 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\qmultiPochhammersym{e/a,f/a}{q}{n}}{\qmultiPochhammersym{e,f}{q}{n}}a^{n}\qgenhyperphi{4}{3}@@{q^{-n},a,d/b,d/c}{d,aq^{1-n}/e,aq^{1-n}/f}{q}{q} = \frac{\qmultiPochhammersym{a,ef/(ab),ef/(ac)}{q}{n}}{\qmultiPochhammersym{e,f,ef/(abc)}{q}{n}}\qgenhyperphi{4}{3}@@{q^{-n},e/a,f/a,ef/(abc)}{ef/(ab),ef/(ac),q^{1-n}/a}{q}{q}} | Error |
Divide[Product[QPochhammer[Part[{e/ a , f/ a},i],q,n],{i,1,Length[{e/ a , f/ a}]}],Product[QPochhammer[Part[{e , f},i],q,n],{i,1,Length[{e , f}]}]]*(a)^(n)* QHypergeometricPFQ[{(q)^(- n), a , d/ b , d/ c},{d , a*(q)^(1 - n)/ e , a*(q)^(1 - n)/ f},q,q] == Divide[Product[QPochhammer[Part[{a , e*f/(a*b), e*f/(a*c)},i],q,n],{i,1,Length[{a , e*f/(a*b), e*f/(a*c)}]}],Product[QPochhammer[Part[{e , f , e*f/(a*b*c)},i],q,n],{i,1,Length[{e , f , e*f/(a*b*c)}]}]]*QHypergeometricPFQ[{(q)^(- n), e/ a , f/ a , e*f/(a*b*c)},{e*f/(a*b), e*f/(a*c), (q)^(1 - n)/ a},q,q] |
Error | Failure | - | Skipped - Because timed out |
| 17.9.E15 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{\qmultiPochhammersym{aq,aq/(de)}{q}{n}}{\qmultiPochhammersym{aq/d,aq/e}{q}{n}}\qgenhyperphi{4}{3}@@{aq/(bc),d,e,q^{-n}}{aq/b,aq/c,deq^{-n}/a}{q}{q} = \qgenhyperphi{8}{7}@@{a,qa^{\frac{1}{2}},-qa^{\frac{1}{2}},b,c,d,e,q^{-n}}{a^{\frac{1}{2}},-a^{\frac{1}{2}},aq/b,aq/c,aq/d,aq/e,aq^{n+1}}{q}{\frac{a^{2}q^{2+n}}{bcde}}} | Error |
Divide[Product[QPochhammer[Part[{a*q , a*q/(d*e)},i],q,n],{i,1,Length[{a*q , a*q/(d*e)}]}],Product[QPochhammer[Part[{a*q/ d , a*q/ e},i],q,n],{i,1,Length[{a*q/ d , a*q/ e}]}]]*QHypergeometricPFQ[{a*q/(b*c), d , e , (q)^(- n)},{a*q/ b , a*q/ c , d*e*(q)^(- n)/ a},q,q] == QHypergeometricPFQ[{a , q*(a)^(Divide[1,2]), - q*(a)^(Divide[1,2]), b , c , d , e , (q)^(- n)},{(a)^(Divide[1,2]), - (a)^(Divide[1,2]), a*q/ b , a*q/ c , a*q/ d , a*q/ e , a*(q)^(n + 1)},q,Divide[(a)^(2)* (q)^(2 + n),b*c*d*e]] |
Error | Failure | - | Failed [240 / 300]
{Plus[Times[Complex[0.9356921938165307, -5.551115123125783*^-17], QHypergeometricPFQ[{Complex[-0.5773502691896257, -0.33333333333333326], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, -0.49999999999999994]} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.5773502691896257, -0.3333333333333332]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], Times[-1.0, QHypergeometricPFQ[{-1.5, Complex[-0.6123724356957944, 1.0606601717798212], Complex[0.6123724356957944, -1.0606601717798212], -1.5, -1.5, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, -0.49999999999999994]}, {Complex[0.0, 1.224744871391589], Complex[0.0, -1.224744871391589], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[-1.5, 0.0], Complex[-1.5, 0.0], Complex[-0.7500000000000002, -1.299038105676658]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844386, 0.5000000000000002]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Times[Complex[0.8717526973154065, 0.006872752237161106], QHypergeometricPFQ[{Complex[-0.5773502691896257, -0.33333333333333326], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.5000000000000001, -0.8660254037844386]} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.6666666666666666, 0.0]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], Times[-1.0, QHypergeometricPFQ[{-1.5, Complex[-0.6123724356957944, 1.0606601717798212], Complex[0.6123724356957944, -1.0606601717798212], -1.5, -1.5, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.5000000000000001, -0.8660254037844386]}, {Complex[0.0, 1.224744871391589], Complex[0.0, -1.224744871391589], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[-1.5, 0.0], Complex[-1.5, 0.0], Complex[0.0, -1.5]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.5, 0.8660254037844386]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]} |
| 17.9.E16 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{8}{7}@@{a,qa^{\frac{1}{2}},-qa^{\frac{1}{2}},b,c,d,e,f}{a^{\frac{1}{2}},-a^{\frac{1}{2}},aq/b,aq/c,aq/d,aq/e,aq/f}{q}{\frac{a^{2}q^{2}}{bcdef}} = \frac{\qmultiPochhammersym{aq,aq/(de),aq/(df),aq/(ef)}{q}{\infty}}{\qmultiPochhammersym{aq/d,aq/e,aq/f,aq/(def)}{q}{\infty}}\qgenhyperphi{4}{3}@@{aq/(bc),d,e,f}{aq/b,aq/c,def/a}{q}{q}+\frac{\qmultiPochhammersym{aq,aq/(bc),d,e,f,a^{2}q^{2}/(bdef),a^{2}q^{2}/(cdef)}{q}{\infty}}{\qmultiPochhammersym{aq/b,aq/c,aq/d,aq/e,aq/f,a^{2}q^{2}/(bcdef),def/(aq)}{q}{\infty}}\*\qgenhyperphi{4}{3}@@{aq/(de),aq/(df),aq/(ef),a^{2}q^{2}/(bcdef)}{a^{2}q^{2}/(bdef),a^{2}q^{2}/(cdef),aq^{2}/(def)}{q}{q}} | Error |
QHypergeometricPFQ[{a , q*(a)^(Divide[1,2]), - q*(a)^(Divide[1,2]), b , c , d , e , f},{(a)^(Divide[1,2]), - (a)^(Divide[1,2]), a*q/ b , a*q/ c , a*q/ d , a*q/ e , a*q/ f},q,Divide[(a)^(2)* (q)^(2),b*c*d*e*f]] == Divide[Product[QPochhammer[Part[{a*q , a*q/(d*e), a*q/(d*f), a*q/(e*f)},i],q,Infinity],{i,1,Length[{a*q , a*q/(d*e), a*q/(d*f), a*q/(e*f)}]}],Product[QPochhammer[Part[{a*q/ d , a*q/ e , a*q/ f , a*q/(d*e*f)},i],q,Infinity],{i,1,Length[{a*q/ d , a*q/ e , a*q/ f , a*q/(d*e*f)}]}]]*QHypergeometricPFQ[{a*q/(b*c), d , e , f},{a*q/ b , a*q/ c , d*e*f/ a},q,q]+Divide[Product[QPochhammer[Part[{a*q , a*q/(b*c), d , e , f , (a)^(2)* (q)^(2)/(b*d*e*f), (a)^(2)* (q)^(2)/(c*d*e*f)},i],q,Infinity],{i,1,Length[{a*q , a*q/(b*c), d , e , f , (a)^(2)* (q)^(2)/(b*d*e*f), (a)^(2)* (q)^(2)/(c*d*e*f)}]}],Product[QPochhammer[Part[{a*q/ b , a*q/ c , a*q/ d , a*q/ e , a*q/ f , (a)^(2)* (q)^(2)/(b*c*d*e*f), d*e*f/(a*q)},i],q,Infinity],{i,1,Length[{a*q/ b , a*q/ c , a*q/ d , a*q/ e , a*q/ f , (a)^(2)* (q)^(2)/(b*c*d*e*f), d*e*f/(a*q)}]}]]* QHypergeometricPFQ[{a*q/(d*e), a*q/(d*f), a*q/(e*f), (a)^(2)* (q)^(2)/(b*c*d*e*f)},{(a)^(2)* (q)^(2)/(b*d*e*f), (a)^(2)* (q)^(2)/(c*d*e*f), a*(q)^(2)/(d*e*f)},q,q] |
Error | Failure | - | Skipped - Because timed out |
| 17.9.E17 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qgenhyperphi{3}{2}@@{a,b,c}{aq/b,aq/c}{q}{\frac{aqz}{bc}} = \frac{\qPochhammer{az}{q}{\infty}}{\qPochhammer{z}{q}{\infty}}\*\qgenhyperphi{5}{4}@@{a^{\frac{1}{2}},-a^{\frac{1}{2}},(aq)^{\frac{1}{2}},-(aq)^{\frac{1}{2}},aq/(bc)}{aq/b,aq/c,az,q/z}{q}{q}} | Error |
QHypergeometricPFQ[{a , b , c},{a*q/ b , a*q/ c},q,Divide[a*q*z,b*c]] == Divide[QPochhammer[a*z, q, Infinity],QPochhammer[z, q, Infinity]]* QHypergeometricPFQ[{(a)^(Divide[1,2]), - (a)^(Divide[1,2]),(a*q)^(Divide[1,2]), -(a*q)^(Divide[1,2]), a*q/(b*c)},{a*q/ b , a*q/ c , a*z , q/ z},q,q] |
Error | Failure | - | Failed [298 / 300]
{Plus[QHypergeometricPFQ[{-1.5, -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.33333333333333337, -0.5773502691896257]], Times[-1.0, QHypergeometricPFQ[{Complex[0.0, 1.224744871391589], Complex[0.0, -1.224744871391589], Complex[0.31698729810778065, -1.1830127018922192], Complex[-0.31698729810778065, 1.1830127018922192], Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[-1.299038105676658, -0.7499999999999999], 1.0}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], QPochhammer[Complex[-1.299038105676658, -0.7499999999999999], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[QHypergeometricPFQ[{-1.5, -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.5773502691896256, -0.3333333333333335]], Times[-1.0, QHypergeometricPFQ[{Complex[0.0, 1.224744871391589], Complex[0.0, -1.224744871391589], Complex[0.31698729810778065, -1.1830127018922192], Complex[-0.31698729810778065, 1.1830127018922192], Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.7499999999999997, -1.299038105676658], Complex[0.0, -1.0]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Power[QPochhammer[Complex[-0.4999999999999998, 0.8660254037844387], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[0.7499999999999997, -1.299038105676658], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.9.E18 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\qgenhyperphi{4}{3}@@{a,b,abz,ab/z}{abq^{\frac{1}{2}},-abq^{\frac{1}{2}},-ab}{q}{q}\right)^{2} = \qgenhyperphi{5}{4}@@{a^{2},b^{2},ab,abz,ab/z}{abq^{\frac{1}{2}},-abq^{\frac{1}{2}},-ab,a^{2}b^{2}}{q}{q}} | Error |
(QHypergeometricPFQ[{a , b , a*b*z , a*b/ z},{a*b*(q)^(Divide[1,2]), - a*b*(q)^(Divide[1,2]), - a*b},q,q])^(2) == QHypergeometricPFQ[{(a)^(2), (b)^(2), a*b , a*b*z , a*b/ z},{a*b*(q)^(Divide[1,2]), - a*b*(q)^(Divide[1,2]), - a*b , (a)^(2)* (b)^(2)},q,q] |
Error | Failure | - | Failed [284 / 300]
{Plus[Power[QHypergeometricPFQ[{-1.5, -1.5, Complex[1.948557158514987, 1.1249999999999998], Complex[1.948557158514987, -1.1249999999999998]} <- {Complex[2.173333109150404, 0.5823428514806717], Complex[-2.173333109150404, -0.5823428514806717], -2.25}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], 2], Times[-1.0, QHypergeometricPFQ[{2.25, 2.25, 2.25, Complex[1.948557158514987, 1.1249999999999998], Complex[1.948557158514987, -1.1249999999999998]}, {Complex[2.173333109150404, 0.5823428514806717], Complex[-2.173333109150404, -0.5823428514806717], -2.25, 5.0625}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}Plus[Power[QHypergeometricPFQ[{-1.5, -1.5, Complex[-1.1249999999999996, 1.948557158514987], Complex[-1.1249999999999996, -1.948557158514987]} <- {Complex[2.173333109150404, 0.5823428514806717], Complex[-2.173333109150404, -0.5823428514806717], -2.25}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], 2], Times[-1.0, QHypergeometricPFQ[{2.25, 2.25, 2.25, Complex[-1.1249999999999996, 1.948557158514987], Complex[-1.1249999999999996, -1.948557158514987]}, {Complex[2.173333109150404, 0.5823428514806717], Complex[-2.173333109150404, -0.5823428514806717], -2.25, 5.0625}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]} |
| 17.9.E19 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\frac{\qPochhammer{a}{q^{2}}{n}\qPochhammer{b}{q}{n}}{\qPochhammer{q^{2}}{q^{2}}{n}\qPochhammer{c}{q}{n}}z^{n} = \frac{\qPochhammer{b}{q}{\infty}\qPochhammer{az}{q^{2}}{\infty}}{\qPochhammer{c}{q}{\infty}\qPochhammer{z}{q^{2}}{\infty}}\sum_{n=0}^{\infty}\frac{\qPochhammer{c/b}{q}{2n}\qPochhammer{z}{q^{2}}{n}b^{2n}}{\qPochhammer{q}{q}{2n}\qPochhammer{az}{q^{2}}{n}}+\frac{\qPochhammer{b}{q}{\infty}\qPochhammer{azq}{q^{2}}{\infty}}{\qPochhammer{c}{q}{\infty}\qPochhammer{zq}{q^{2}}{\infty}}\sum_{n=0}^{\infty}\frac{\qPochhammer{c/b}{q}{2n+1}\qPochhammer{zq}{q^{2}}{n}b^{2n+1}}{\qPochhammer{q}{q}{2n+1}\qPochhammer{azq}{q^{2}}{n}}} | sum((QPochhammer(a, (q)^(2), n)*QPochhammer(b, q, n))/(QPochhammer((q)^(2), (q)^(2), n)*QPochhammer(c, q, n))*(z)^(n), n = 0..infinity) = (QPochhammer(b, q, infinity)*QPochhammer(a*z, (q)^(2), infinity))/(QPochhammer(c, q, infinity)*QPochhammer(z, (q)^(2), infinity))*sum((QPochhammer(c/ b, q, 2*n)*QPochhammer(z, (q)^(2), n)*(b)^(2*n))/(QPochhammer(q, q, 2*n)*QPochhammer(a*z, (q)^(2), n)), n = 0..infinity)+(QPochhammer(b, q, infinity)*QPochhammer(a*z*q, (q)^(2), infinity))/(QPochhammer(c, q, infinity)*QPochhammer(z*q, (q)^(2), infinity))*sum((QPochhammer(c/ b, q, 2*n + 1)*QPochhammer(z*q, (q)^(2), n)*(b)^(2*n + 1))/(QPochhammer(q, q, 2*n + 1)*QPochhammer(a*z*q, (q)^(2), n)), n = 0..infinity) |
Sum[Divide[QPochhammer[a, (q)^(2), n]*QPochhammer[b, q, n],QPochhammer[(q)^(2), (q)^(2), n]*QPochhammer[c, q, n]]*(z)^(n), {n, 0, Infinity}, GenerateConditions->None] == Divide[QPochhammer[b, q, Infinity]*QPochhammer[a*z, (q)^(2), Infinity],QPochhammer[c, q, Infinity]*QPochhammer[z, (q)^(2), Infinity]]*Sum[Divide[QPochhammer[c/ b, q, 2*n]*QPochhammer[z, (q)^(2), n]*(b)^(2*n),QPochhammer[q, q, 2*n]*QPochhammer[a*z, (q)^(2), n]], {n, 0, Infinity}, GenerateConditions->None]+Divide[QPochhammer[b, q, Infinity]*QPochhammer[a*z*q, (q)^(2), Infinity],QPochhammer[c, q, Infinity]*QPochhammer[z*q, (q)^(2), Infinity]]*Sum[Divide[QPochhammer[c/ b, q, 2*n + 1]*QPochhammer[z*q, (q)^(2), n]*(b)^(2*n + 1),QPochhammer[q, q, 2*n + 1]*QPochhammer[a*z*q, (q)^(2), n]], {n, 0, Infinity}, GenerateConditions->None] |
Failure | Error | Error | Skipped - Because timed out |
| 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(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(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(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((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 | Error | Error | Failed [300 / 300]
{Complex[0.6508376433032488, -0.21856268949920582] <- {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]]]}Complex[0.8660402331469415, 0.20457300495175623] <- {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]]]} |
| 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((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 | Error | 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] = (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]
{Complex[5.814582562299427, -3.4240381056766607] <- {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]]]}Complex[-12.010896071760529, -4.7481964481437355] <- {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]]]} |
| 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] = (1)/(QPochhammer(q, q, n)) |
Subscript[\[Beta], n] == Divide[1,QPochhammer[q, q, n]] |
Failure | Failure | Error | Failed [297 / 300]
{Complex[0.3660254037844387, -1.366025403784439] <- {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]]]}Complex[2.232050807568878, -0.8660254037844388] <- {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]]]} |
| 17.13.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \int_{0}^{\infty}t^{\alpha-1}\frac{\qPochhammer{-tq^{\alpha+\beta}}{q}{\infty}}{\qPochhammer{-t}{q}{\infty}}\diff{t} = \frac{\EulerGamma@{\alpha}\EulerGamma@{1-\alpha}\qGamma{q}@{\beta}}{\qGamma{q}@{1-\alpha}\qGamma{q}@{\alpha+\beta}}} | int((t)^(alpha - 1)*(QPochhammer(- t*(q)^(alpha + beta), q, infinity))/(QPochhammer(- t, q, infinity)), t = 0..infinity) = (GAMMA(alpha)*GAMMA(1 - alpha)*QGAMMA(q, beta))/(QGAMMA(q, 1 - alpha)*QGAMMA(q, alpha + beta)) |
Integrate[(t)^(\[Alpha]- 1)*Divide[QPochhammer[- t*(q)^(\[Alpha]+ \[Beta]), q, Infinity],QPochhammer[- t, q, Infinity]], {t, 0, Infinity}, GenerateConditions->None] == Divide[Gamma[\[Alpha]]*Gamma[1 - \[Alpha]]*QGamma[\[Beta],q],QGamma[1 - \[Alpha],q]*QGamma[\[Alpha]+ \[Beta],q]] |
Error | Failure | - | Failed [26 / 30]
{Plus[NIntegrate[Times[Power[t, -0.5], Power[QPochhammer[Times[-1, t], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], DirectedInfinity[1]], -1], QPochhammer[Times[Complex[-0.5000000000000001, -0.8660254037844386], t], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], DirectedInfinity[1]]] <- {t, 0, DirectedInfinity[1]}], Times[-3.1415926535897936, Power[QGamma[0.5, Complex[0.8660254037844387, 0.49999999999999994]], -1], QGamma[1.5, Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5], Rule[β, 1.5]}Plus[-3.1415926535897936, NIntegrate[Times[Power[t, -0.5], Power[QPochhammer[Times[-1, t], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], DirectedInfinity[1]], -1], QPochhammer[Times[Complex[-0.8660254037844387, -0.49999999999999994], t], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], DirectedInfinity[1]]] <- {t, 0, DirectedInfinity[1]}]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5], Rule[β, 0.5]} |