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| |- | | ; Notation : [[17.1|17.1 Special Notation]]<br> |
| ! DLMF !! Formula !! Constraints !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica
| | ; Properties : [[17.2|17.2 Calculus]]<br>[[17.3|17.3 <math>q</math> -Elementary and <math>q</math> -Special Functions]]<br>[[17.4|17.4 Basic Hypergeometric Functions]]<br>[[17.5|17.5 <math>\qgenhyperphi{0}{0},\qgenhyperphi{1}{0},\qgenhyperphi{1}{1}</math> Functions]]<br>[[17.6|17.6 <math>\qgenhyperphi{2}{1}</math> Function]]<br>[[17.7|17.7 Special Cases of Higher <math>\qgenhyperphi{r}{s}</math> Functions]]<br>[[17.8|17.8 Special Cases of <math>\qgenhyperpsi{r}{r}</math> Functions]]<br>[[17.9|17.9 Further Transformations of <math>\qgenhyperphi{r+1}{r}</math> Functions]]<br>[[17.10|17.10 Transformations of <math>\qgenhyperpsi{r}{r}</math> Functions]]<br>[[17.11|17.11 Transformations of <math>q</math> -Appell Functions]]<br>[[17.12|17.12 Bailey Pairs]]<br>[[17.13|17.13 Integrals]]<br>[[17.14|17.14 Constant Term Identities]]<br>[[17.15|17.15 Generalizations]]<br> |
| |-
| | ; Applications : [[17.16|17.16 Mathematical Applications]]<br>[[17.17|17.17 Physical Applications]]<br> |
| | [https://dlmf.nist.gov/17.2.E2 17.2.E2] || [[Item:Q5292|<math>\qPochhammer{a}{q}{-n} = \frac{1}{\qPochhammer{aq^{-n}}{q}{n}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>QPochhammer(a, q, - n) = (1)/(QPochhammer(a*(q)^(- n), q, n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>QPochhammer[a, q, - n] == Divide[1,QPochhammer[a*(q)^(- n), q, n]]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
| | ; Computation : [[17.18|17.18 Methods of Computation]]<br>[[17.19|17.19 Software]]<br> |
| Test Values: {Rule[a, -1.5], Rule[n, 1], Rule[q, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
| | </div> |
| Test Values: {Rule[a, -1.5], Rule[n, 2], Rule[q, -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.2.E2 17.2.E2] || [[Item:Q5292|<math>\frac{1}{\qPochhammer{aq^{-n}}{q}{n}} = \frac{(-q/a)^{n}q^{\binom{n}{2}}}{\qPochhammer{q/a}{q}{n}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(1)/(QPochhammer(a*(q)^(- n), q, n)) = ((- q/a)^(n)* (q)^(binomial(n,2)))/(QPochhammer(q/a, q, n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,QPochhammer[a*(q)^(- n), q, n]] == Divide[(- q/a)^(n)* (q)^(Binomial[n,2]),QPochhammer[q/a, q, n]]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 180]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[n, 1], Rule[q, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[n, 2], Rule[q, -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.2.E3 17.2.E3] || [[Item:Q5293|<math>\qPochhammer{a}{q}{\nu} = \prod_{j=0}^{\infty}\left(\frac{1-aq^{j}}{1-aq^{\nu+j}}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>QPochhammer(a, q, nu) = product((1 - a*(q)^(j))/(1 - a*(q)^(nu + j)), j = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>QPochhammer[a, q, \[Nu]] == Product[Divide[1 - a*(q)^(j),1 - a*(q)^(\[Nu]+ j)], {j, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [33 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {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]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.2.E4 17.2.E4] || [[Item:Q5294|<math>\qPochhammer{a}{q}{\infty} = \prod_{j=0}^{\infty}(1-aq^{j})</math>]] || <math></math> || <syntaxhighlight lang=mathematica>QPochhammer(a, q, infinity) = product(1 - a*(q)^(j), j = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>QPochhammer[a, q, Infinity] == Product[1 - a*(q)^(j), {j, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [48 / 60]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Times[-1.0, QPochhammer[-1.5, Complex[0.8660254037844387, 0.49999999999999994]]], QPochhammer[-1.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]
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| Test Values: {Rule[a, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.2.E7 17.2.E7] || [[Item:Q5297|<math>\qPochhammer{a}{q^{-1}}{n} = \qPochhammer{a^{-1}}{q}{n}(-a)^{n}q^{-\binom{n}{2}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>QPochhammer(a, (q)^(- 1), n) = QPochhammer((a)^(- 1), q, n)*(- a)^(n)* (q)^(-binomial(n,2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>QPochhammer[a, (q)^(- 1), n] == QPochhammer[(a)^(- 1), q, n]*(- a)^(n)* (q)^(-Binomial[n,2])</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 180]
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| | [https://dlmf.nist.gov/17.2.E8 17.2.E8] || [[Item:Q5298|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(QPochhammer(a, (q)^(- 1), n))/(QPochhammer(b, (q)^(- 1), n)) = (QPochhammer((a)^(- 1), q, n))/(QPochhammer((b)^(- 1), q, n))*((a)/(b))^(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[q, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 3], Rule[q, -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.2.E9 17.2.E9] || [[Item:Q5299|<math>\qPochhammer{a}{q}{n} = \qPochhammer{q^{1-n}/a}{q}{n}(-a)^{n}q^{\binom{n}{2}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>QPochhammer(a, q, n) = QPochhammer((q)^(1 - n)/a, q, n)*(- a)^(n)* (q)^(binomial(n,2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>QPochhammer[a, q, n] == QPochhammer[(q)^(1 - n)/a, q, n]*(- a)^(n)* (q)^(Binomial[n,2])</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 180]
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| | [https://dlmf.nist.gov/17.2.E10 17.2.E10] || [[Item:Q5300|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [12 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[b, -0.5], Rule[n, 2], Rule[q, -2]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[b, -0.5], Rule[n, 3], Rule[q, -2]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.2.E11 17.2.E11] || [[Item:Q5301|<math>\qPochhammer{aq^{-n}}{q}{n} = \qPochhammer{q/a}{q}{n}\left(-\frac{a}{q}\right)^{n}q^{-\binom{n}{2}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>QPochhammer(a*(q)^(- n), q, n) = QPochhammer(q/a, q, n)*(-(a)/(q))^(n)* (q)^(-binomial(n,2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>QPochhammer[a*(q)^(- n), q, n] == QPochhammer[q/a, q, n]*(-Divide[a,q])^(n)* (q)^(-Binomial[n,2])</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 180]
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| | [https://dlmf.nist.gov/17.2.E12 17.2.E12] || [[Item:Q5302|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[q, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[q, -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.2.E13 17.2.E13] || [[Item:Q5303|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [14 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[k, 2], Rule[n, 1], Rule[q, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[k, 3], Rule[n, 1], Rule[q, -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.2.E14 17.2.E14] || [[Item:Q5304|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [15 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 2], Rule[n, 1], Rule[q, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 3], Rule[n, 1], Rule[q, -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.2.E15 17.2.E15] || [[Item:Q5305|<math>\qPochhammer{aq^{-n}}{q}{k} = \frac{\qPochhammer{a}{q}{k}\qPochhammer{q/a}{q}{n}}{\qPochhammer{q^{1-k}/a}{q}{n}}q^{-nk}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [14 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[n, 2], Rule[q, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[n, 3], Rule[q, -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.2.E16 17.2.E16] || [[Item:Q5306|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [27 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[n, 1], Rule[q, -1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[k, 1], Rule[n, 2], Rule[q, -1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.2.E17 17.2.E17] || [[Item:Q5307|<math>\qPochhammer{aq^{n}}{q}{k} = \frac{\qPochhammer{a}{q}{k}\qPochhammer{aq^{k}}{q}{n}}{\qPochhammer{a}{q}{n}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>QPochhammer(a*(q)^(n), q, k) = (QPochhammer(a, q, k)*QPochhammer(a*(q)^(k), q, n))/(QPochhammer(a, q, n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>QPochhammer[a*(q)^(n), q, k] == Divide[QPochhammer[a, q, k]*QPochhammer[a*(q)^(k), q, n],QPochhammer[a, q, n]]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -0.5], Rule[k, 1], Rule[n, 2], Rule[q, -2]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -0.5], Rule[k, 1], Rule[n, 3], Rule[q, -2]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.2.E18 17.2.E18] || [[Item:Q5308|<math>\qPochhammer{aq^{k}}{q}{n-k} = \frac{\qPochhammer{a}{q}{n}}{\qPochhammer{a}{q}{k}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>QPochhammer(a*(q)^(k), q, n - k) = (QPochhammer(a, q, n))/(QPochhammer(a, q, k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>QPochhammer[a*(q)^(k), q, n - k] == Divide[QPochhammer[a, q, n],QPochhammer[a, q, k]]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -0.5], Rule[k, 2], Rule[n, 1], Rule[q, -2]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -0.5], Rule[k, 2], Rule[n, 2], Rule[q, -2]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.2.E19 17.2.E19] || [[Item:Q5309|<math>\qPochhammer{a}{q}{2n} = \qmultiPochhammersym{a,aq}{q^{2}}{n}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>QPochhammer[a, q, 2*n] == Product[QPochhammer[Part[{a , a*q},i],(q)^(2),n],{i,1,Length[{a , a*q}]}]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 180]
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| | [https://dlmf.nist.gov/17.2.E21 17.2.E21] || [[Item:Q5311|<math>\qPochhammer{a^{2}}{q^{2}}{n} = \qPochhammer{a}{q}{n}\qPochhammer{-a}{q}{n}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>QPochhammer((a)^(2), (q)^(2), n) = QPochhammer(a, q, n)*QPochhammer(- a, q, n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>QPochhammer[(a)^(2), (q)^(2), n] == QPochhammer[a, q, n]*QPochhammer[- a, q, n]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 180]
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| | [https://dlmf.nist.gov/17.2.E22 17.2.E22] || [[Item:Q5312|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 180]
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| | [https://dlmf.nist.gov/17.2.E22 17.2.E22] || [[Item:Q5312|<math>\frac{\qPochhammer{aq^{2}}{q^{2}}{n}}{\qPochhammer{a}{q^{2}}{n}} = \frac{1-aq^{2n}}{1-a}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(QPochhammer(a*(q)^(2), (q)^(2), n))/(QPochhammer(a, (q)^(2), n)) = (1 - a*(q)^(2*n))/(1 - a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[QPochhammer[a*(q)^(2), (q)^(2), n],QPochhammer[a, (q)^(2), n]] == Divide[1 - a*(q)^(2*n),1 - a]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 180]
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| | [https://dlmf.nist.gov/17.2.E23 17.2.E23] || [[Item:Q5313|<math>\frac{\qPochhammer{aq^{k}}{q^{k}}{n}}{\qPochhammer{a}{q^{k}}{n}} = \frac{1-aq^{kn}}{1-a}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(QPochhammer(a*(q)^(k), (q)^(k), n))/(QPochhammer(a, (q)^(k), n)) = (1 - a*(q)^(k*n))/(1 - a)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[QPochhammer[a*(q)^(k), (q)^(k), n],QPochhammer[a, (q)^(k), n]] == Divide[1 - a*(q)^(k*n),1 - a]</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -0.5], Rule[k, 1], Rule[n, 2], Rule[q, -2]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -0.5], Rule[k, 1], Rule[n, 3], Rule[q, -2]}</syntaxhighlight><br></div></div>
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| | [https://dlmf.nist.gov/17.2.E24 17.2.E24] || [[Item:Q5314|<math>\lim_{\tau\to 0}\qPochhammer{a/\tau}{q}{n}\tau^{n} = \lim_{\sigma\to\infty}\qPochhammer{a\sigma}{q}{n}\sigma^{-n}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>limit(QPochhammer(a/tau, q, n)*(tau)^(n), tau = 0) = limit(QPochhammer(a*sigma, q, n)*(sigma)^(- n), sigma = infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[QPochhammer[a/\[Tau], q, n]*\[Tau]^(n), \[Tau] -> 0, GenerateConditions->None] == Limit[QPochhammer[a*\[Sigma], q, n]*\[Sigma]^(- n), \[Sigma] -> Infinity, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 180]
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| |-
| |
| | [https://dlmf.nist.gov/17.2.E24 17.2.E24] || [[Item:Q5314|<math>\lim_{\sigma\to\infty}\qPochhammer{a\sigma}{q}{n}\sigma^{-n} = (-a)^{n}q^{\binom{n}{2}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>limit(QPochhammer(a*sigma, q, n)*(sigma)^(- n), sigma = infinity) = (- a)^(n)* (q)^(binomial(n,2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[QPochhammer[a*\[Sigma], q, n]*\[Sigma]^(- n), \[Sigma] -> Infinity, GenerateConditions->None] == (- a)^(n)* (q)^(Binomial[n,2])</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 180]
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| | [https://dlmf.nist.gov/17.2.E25 17.2.E25] || [[Item:Q5315|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 300]
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| |
| | [https://dlmf.nist.gov/17.2.E25 17.2.E25] || [[Item:Q5315|<math>\lim_{\sigma\to\infty}\frac{\qPochhammer{a\sigma}{q}{n}}{\qPochhammer{b\sigma}{q}{n}} = \left(\frac{a}{b}\right)^{n}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>limit((QPochhammer(a*sigma, q, n))/(QPochhammer(b*sigma, q, n)), sigma = infinity) = ((a)/(b))^(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[Divide[QPochhammer[a*\[Sigma], q, n],QPochhammer[b*\[Sigma], q, n]], \[Sigma] -> Infinity, GenerateConditions->None] == (Divide[a,b])^(n)</syntaxhighlight> || Failure || Failure || Error || Successful [Tested: 300]
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| | [https://dlmf.nist.gov/17.2.E26 17.2.E26] || [[Item:Q5316|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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])</syntaxhighlight> || Error || Failure || - || Successful [Tested: 300]
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| | [https://dlmf.nist.gov/17.2.E27 17.2.E27] || [[Item:Q5317|<math>\qbinom{n}{m}{q} = \frac{\qPochhammer{q}{q}{n}}{\qPochhammer{q}{q}{m}\qPochhammer{q}{q}{n-m}}\\</math>]] || <math></math> || <syntaxhighlight lang=mathematica>QBinomial(n, m, q) = (QPochhammer(q, q, n))/(QPochhammer(q, q, m)*QPochhammer(q, q, n - m))</syntaxhighlight> || <syntaxhighlight lang=mathematica>QBinomial[n,m,q] == Divide[QPochhammer[q, q, n],QPochhammer[q, q, m]*QPochhammer[q, q, n - m]]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.058394160583941646, 0.1605839416058394]
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| Test Values: {Rule[m, 3], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br></div></div>
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| | [https://dlmf.nist.gov/17.2.E27 17.2.E27] || [[Item:Q5317|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.11678832116788332, -0.3211678832116788]
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| Test Values: {Rule[m, 3], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.0, 0.0]
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| Test Values: {Rule[m, 3], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| |-
| |
| | [https://dlmf.nist.gov/17.2.E28 17.2.E28] || [[Item:Q5318|<math>\lim_{q\to 1}\qbinom{n}{m}{q} = \binom{n}{m}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>limit(QBinomial(n, m, q), q = 1) = binomial(n,m)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[QBinomial[n,m,q], q -> 1, GenerateConditions->None] == Binomial[n,m]</syntaxhighlight> || Failure || Aborted || Error || Skipped - Because timed out
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| |-
| |
| | [https://dlmf.nist.gov/17.2.E28 17.2.E28] || [[Item:Q5318|<math>\binom{n}{m} = \frac{n!}{m!(n-m)!}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>binomial(n,m) = (factorial(n))/(factorial(m)*factorial(n - m))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Binomial[n,m] == Divide[(n)!,(m)!*(n - m)!]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 9]
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| |-
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| | [https://dlmf.nist.gov/17.2.E29 17.2.E29] || [[Item:Q5319|<math>\qbinom{m+n}{m}{q} = \frac{\qPochhammer{q^{n+1}}{q}{m}}{\qPochhammer{q}{q}{m}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>QBinomial(m + n, m, q) = (QPochhammer((q)^(n + 1), q, m))/(QPochhammer(q, q, m))</syntaxhighlight> || <syntaxhighlight lang=mathematica>QBinomial[m + n,m,q] == Divide[QPochhammer[(q)^(n + 1), q, m],QPochhammer[q, q, m]]</syntaxhighlight> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [3 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.9416058394160581, 0.1605839416058394]
| |
| Test Values: {Rule[m, 3], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[1.0, 0.0]
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| Test Values: {Rule[m, 3], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| |-
| |
| | [https://dlmf.nist.gov/17.2.E30 17.2.E30] || [[Item:Q5320|<math>\qbinom{-n}{m}{q} = \qbinom{m+n-1}{m}{q}(-1)^{m}q^{-mn-\binom{m}{2}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>QBinomial(- n, m, q) = QBinomial(m + n - 1, m, q)*(- 1)^(m)* (q)^(- m*n -binomial(m,2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>QBinomial[- n,m,q] == QBinomial[m + n - 1,m,q]*(- 1)^(m)* (q)^(- m*n -Binomial[m,2])</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [84 / 90]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.7320508075688774, 0.0]
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| Test Values: {Rule[m, 1], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.3660254037844384, -1.3660254037844386]
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| Test Values: {Rule[m, 1], Rule[n, 3], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.2.E31 17.2.E31] || [[Item:Q5321|<math>\qbinom{n}{m}{q} = \qbinom{n-1}{m-1}{q}+q^{m}\qbinom{n-1}{m}{q}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>QBinomial(n, m, q) = QBinomial(n - 1, m - 1, q)+ (q)^(m)* QBinomial(n - 1, m, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>QBinomial[n,m,q] == QBinomial[n - 1,m - 1,q]+ (q)^(m)* QBinomial[n - 1,m,q]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 90]
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| |-
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| | [https://dlmf.nist.gov/17.2.E32 17.2.E32] || [[Item:Q5322|<math>\qbinom{n}{m}{q} = \qbinom{n-1}{m}{q}+q^{n-m}\qbinom{n-1}{m-1}{q}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>QBinomial(n, m, q) = QBinomial(n - 1, m, q)+ (q)^(n - m)* QBinomial(n - 1, m - 1, q)</syntaxhighlight> || <syntaxhighlight lang=mathematica>QBinomial[n,m,q] == QBinomial[n - 1,m,q]+ (q)^(n - m)* QBinomial[n - 1,m - 1,q]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 90]
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| |-
| |
| | [https://dlmf.nist.gov/17.2.E33 17.2.E33] || [[Item:Q5323|<math>\lim_{n\to\infty}\qbinom{n}{m}{q} = \frac{1}{\qPochhammer{q}{q}{m}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>limit(QBinomial(n, m, q), n = infinity) = (1)/(QPochhammer(q, q, m))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[QBinomial[n,m,q], n -> Infinity, GenerateConditions->None] == Divide[1,QPochhammer[q, q, m]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [24 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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}]]]]]]
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| Test Values: {Rule[m, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 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}]]]]]]
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| Test Values: {Rule[m, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| |-
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| | [https://dlmf.nist.gov/17.2.E34 17.2.E34] || [[Item:Q5324|<math>\lim_{n\to\infty}\qbinom{rn+u}{sn+t}{q} = \frac{1}{\qPochhammer{q}{q}{\infty}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>limit(QBinomial(r*n + u, sn(+)*t, q), n = infinity) = (1)/(QPochhammer(q, q, infinity))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Limit[QBinomial[r*n + u,sn[+]*t,q], n -> Infinity, GenerateConditions->None] == Divide[1,QPochhammer[q, q, Infinity]]</syntaxhighlight> || Error || Failure || Skip - symbolical successful subtest || Error
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| |-
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| | [https://dlmf.nist.gov/17.2.E34 17.2.E34] || [[Item:Q5324|<math>\frac{1}{\qPochhammer{q}{q}{\infty}} = \prod_{j=1}^{\infty}\frac{1}{(1-q^{j})}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>(1)/(QPochhammer(q, q, infinity)) = product((1)/(1 - (q)^(j)), j = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1,QPochhammer[q, q, Infinity]] == Product[Divide[1,1 - (q)^(j)], {j, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]]
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| Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 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]]
| |
| Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| |-
| |
| | [https://dlmf.nist.gov/17.2.E35 17.2.E35] || [[Item:Q5325|<math>\sum_{j=0}^{n}\qbinom{n}{j}{q}(-z)^{j}q^{\binom{j}{2}} = \qPochhammer{z}{q}{n}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum(QBinomial(n, j, q)*(- z)^(j)* (q)^(binomial(j,2)), j = 0..n) = QPochhammer(z, q, n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[QBinomial[n,j,q]*(- z)^(j)* (q)^(Binomial[j,2]), {j, 0, n}, GenerateConditions->None] == QPochhammer[z, q, n]</syntaxhighlight> || Failure || Successful || Error || Successful [Tested: 210]
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| | [https://dlmf.nist.gov/17.2.E36 17.2.E36] || [[Item:Q5326|<math>\sum_{j=0}^{n}\binom{n}{j}(-z)^{j} = (1-z)^{n}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum(binomial(n,j)*(- z)^(j), j = 0..n) = (1 - z)^(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Binomial[n,j]*(- z)^(j), {j, 0, n}, GenerateConditions->None] == (1 - z)^(n)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
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| | [https://dlmf.nist.gov/17.2.E37 17.2.E37] || [[Item:Q5327|<math>\sum_{n=0}^{\infty}\frac{\qPochhammer{a}{q}{n}}{\qPochhammer{q}{q}{n}}z^{n} = \frac{\qPochhammer{az}{q}{\infty}}{\qPochhammer{z}{q}{\infty}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum((QPochhammer(a, q, n))/(QPochhammer(q, q, n))*(z)^(n), n = 0..infinity) = (QPochhammer(a*z, q, infinity))/(QPochhammer(z, q, infinity))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]]]
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| Test Values: {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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Times[Power[QPochhammer[Complex[-0.4999999999999998, 0.8660254037844387], Complex[0.8660254037844387, 0.49999999999999994]], -1], QPochhammer[Complex[0.7499999999999997, -1.299038105676658], Complex[0.866</div></div>
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| |
| | [https://dlmf.nist.gov/17.2.E38 17.2.E38] || [[Item:Q5328|<math>\sum_{n=0}^{\infty}\qbinom{n+m}{n}{q}z^{n} = \frac{1}{\qPochhammer{z}{q}{m+1}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum(QBinomial(n + m, n, q)*(z)^(n), n = 0..infinity) = (1)/(QPochhammer(z, q, m + 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[QBinomial[n + m,n,q]*(z)^(n), {n, 0, Infinity}, GenerateConditions->None] == Divide[1,QPochhammer[z, q, m + 1]]</syntaxhighlight> || Failure || Aborted || Error || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.2.E39 17.2.E39] || [[Item:Q5329|<math>\sum_{j=0}^{n}\qbinom{n}{j}{q^{2}}q^{j} = \qPochhammer{-q}{q}{n}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum(QBinomial(n, j, (q)^(2))*(q)^(j), j = 0..n) = QPochhammer(- q, q, n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[QBinomial[n,j,(q)^(2)]*(q)^(j), {j, 0, n}, GenerateConditions->None] == QPochhammer[- q, q, n]</syntaxhighlight> || Failure || Aborted || Error || Successful [Tested: 30]
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| | [https://dlmf.nist.gov/17.2.E40 17.2.E40] || [[Item:Q5330|<math>\sum_{j=0}^{2n}(-1)^{j}\qbinom{2n}{j}{q} = \qPochhammer{q}{q^{2}}{n}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum((- 1)^(j)* QBinomial(2*n, j, q), j = 0..2*n) = QPochhammer(q, (q)^(2), n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(- 1)^(j)* QBinomial[2*n,j,q], {j, 0, 2*n}, GenerateConditions->None] == QPochhammer[q, (q)^(2), n]</syntaxhighlight> || Failure || Successful || Error || Successful [Tested: 30]
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| |
| | [https://dlmf.nist.gov/17.3.E1 17.3.E1] || [[Item:Q5341|<math>\sum_{n=0}^{\infty}\frac{(1-q)^{n}x^{n}}{\qPochhammer{q}{q}{n}} = \frac{1}{\qPochhammer{(1-q)x}{q}{\infty}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum(((1 - q)^(n)* (x)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = (1)/(QPochhammer((1 - q)*x, q, infinity))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[(1 - q)^(n)* (x)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == Divide[1,QPochhammer[(1 - q)*x, q, Infinity]]</syntaxhighlight> || Failure || Aborted || Error || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.3.E2 17.3.E2] || [[Item:Q5342|<math>\sum_{n=0}^{\infty}\frac{(1-q)^{n}q^{\binom{n}{2}}x^{n}}{\qPochhammer{q}{q}{n}} = \qPochhammer{-(1-q)x}{q}{\infty}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum(((1 - q)^(n)* (q)^(binomial(n,2))* (x)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = QPochhammer(-(1 - q)*x, q, infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Aborted || Error || Skipped - Because timed out
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| |
| | [https://dlmf.nist.gov/17.4.E11 17.4.E11] || [[Item:Q5360|<math>a_{0}q = a_{1}b_{1}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>a[0]*q = a[1]*b[1]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[a, 0]*q == Subscript[a, 1]*Subscript[b, 1]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| | [https://dlmf.nist.gov/17.4.E12 17.4.E12] || [[Item:Q5361|<math>b_{1} = -b_{2}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>b[1] = - b[2]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[b, 1] == - Subscript[b, 2]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| | [https://dlmf.nist.gov/17.4.E13 17.4.E13] || [[Item:Q5362|<math>a_{0}q = a_{1}b_{1}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>a[0]*q = a[1]*b[1]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[a, 0]*q == Subscript[a, 1]*Subscript[b, 1]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| | [https://dlmf.nist.gov/17.5.E1 17.5.E1] || [[Item:Q5363|<math>\qgenhyperphi{0}{0}@{-}{-}{q}{z} = \sum_{n=0}^{\infty}\frac{(-1)^{n}q^{\binom{n}{2}}z^{n}}{\qPochhammer{q}{q}{n}}</math>]] || <math>|z| < 1</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>QHypergeometricPFQ[{-},{-},q,z] == Sum[Divide[(- 1)^(n)* (q)^(Binomial[n,2])* (z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Failure || Skip - symbolical successful subtest || Error
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| |
| | [https://dlmf.nist.gov/17.5.E1 17.5.E1] || [[Item:Q5363|<math>\sum_{n=0}^{\infty}\frac{(-1)^{n}q^{\binom{n}{2}}z^{n}}{\qPochhammer{q}{q}{n}} = \qPochhammer{z}{q}{\infty}</math>]] || <math>|z| < 1</math> || <syntaxhighlight lang=mathematica>sum(((- 1)^(n)* (q)^(binomial(n,2))* (z)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = QPochhammer(z, q, infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[(- 1)^(n)* (q)^(Binomial[n,2])* (z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == QPochhammer[z, q, Infinity]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [8 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[QPochhammer[0.5, Complex[0.8660254037844387, 0.49999999999999994]], Times[-1.0, QPochhammer[0.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]]
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| Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, 0.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[z, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.5.E2 17.5.E2] || [[Item:Q5364|<math>\qgenhyperphi{1}{0}@{a}{-}{q}{z} = \frac{\qPochhammer{az}{q}{\infty}}{\qPochhammer{z}{q}{\infty}}</math>]] || <math>|z| < 1</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>QHypergeometricPFQ[{a},{-},q,z] == Divide[QPochhammer[a*z, q, Infinity],QPochhammer[z, q, Infinity]]</syntaxhighlight> || Missing Macro Error || Failure || - || Error
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| |
| | [https://dlmf.nist.gov/17.5.E3 17.5.E3] || [[Item:Q5365|<math>\qgenhyperphi{1}{0}@{q^{-n}}{-}{q}{z} = \qPochhammer{zq^{-n}}{q}{n}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>QHypergeometricPFQ[{(q)^(- n)},{-},q,z] == QPochhammer[z*(q)^(- n), q, n]</syntaxhighlight> || Missing Macro Error || Failure || - || Error
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| | [https://dlmf.nist.gov/17.5.E4 17.5.E4] || [[Item:Q5366|<math>\qgenhyperphi{1}{0}@{0}{-}{q}{z} = \sum_{n=0}^{\infty}\frac{z^{n}}{\qPochhammer{q}{q}{n}}</math>]] || <math>|z| < 1</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>QHypergeometricPFQ[{0},{-},q,z] == Sum[Divide[(z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Failure || Skip - symbolical successful subtest || Error
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| |
| | [https://dlmf.nist.gov/17.5.E4 17.5.E4] || [[Item:Q5366|<math>\sum_{n=0}^{\infty}\frac{z^{n}}{\qPochhammer{q}{q}{n}} = \frac{1}{\qPochhammer{z}{q}{\infty}}</math>]] || <math>|z| < 1</math> || <syntaxhighlight lang=mathematica>sum(((z)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = (1)/(QPochhammer(z, q, infinity))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[(z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == Divide[1,QPochhammer[z, q, Infinity]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [8 / 10]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[QHypergeometricPFQ[{0.0}
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| Test Values: {}, 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]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: QHypergeometricPFQ[{0.0}
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| Test Values: {}, Complex[-0.4999999999999998, 0.8660254037844387], 0.5], {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[z, 0.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.5.E5 17.5.E5] || [[Item:Q5367|<math>\qgenhyperphi{1}{1}@@{a}{c}{q}{c/a} = \frac{\qPochhammer{c/a}{q}{\infty}}{\qPochhammer{c}{q}{\infty}}</math>]] || <math>|c| < |a|</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>QHypergeometricPFQ[{a},{c},q,c/a] == Divide[QPochhammer[c/a, q, Infinity],QPochhammer[c, q, Infinity]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [96 / 120]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[QHypergeometricPFQ[{-1.5}
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| Test Values: {-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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[c, -0.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.6.E1 17.6.E1] || [[Item:Q5368|<math>\qgenhyperphi{2}{1}@@{a,b}{c}{q}{\ifrac{c}{(ab)}} = \frac{\qmultiPochhammersym{c/a,c/b}{q}{\infty}}{\qmultiPochhammersym{c,c/(ab)}{q}{\infty}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)}]}]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [262 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[0.0, QHypergeometricPFQ[{-1.5, -1.5}
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| Test Values: {-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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[0.0, QHypergeometricPFQ[{-1.5, -1.5}
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| Test Values: {-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]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.6.E2 17.6.E2] || [[Item:Q5369|<math>\qgenhyperphi{2}{1}@@{a,q^{-n}}{c}{q}{\ifrac{cq^{n}}{a}} = \frac{\qPochhammer{c/a}{q}{n}}{\qPochhammer{c}{q}{n}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>QHypergeometricPFQ[{a , (q)^(- n)},{c},q,Divide[c*(q)^(n),a]] == Divide[QPochhammer[c/a, q, n],QPochhammer[c, q, n]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [204 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[0.0, QHypergeometricPFQ[{-1.5, Complex[0.8660254037844387, -0.49999999999999994]}
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| Test Values: {-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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[0.5000000000000001, -0.8660254037844386]}
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| Test Values: {-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]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.6.E3 17.6.E3] || [[Item:Q5370|<math>\qgenhyperphi{2}{1}@@{a,q^{-n}}{c}{q}{q} = \frac{a^{n}\qPochhammer{c/a}{q}{n}}{\qPochhammer{c}{q}{n}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>QHypergeometricPFQ[{a , (q)^(- n)},{c},q,q] == Divide[(a)^(n)* QPochhammer[c/a, q, n],QPochhammer[c, q, n]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [168 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[0.0, QHypergeometricPFQ[{-1.5, Complex[0.8660254037844387, -0.49999999999999994]}
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| Test Values: {-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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[0.5000000000000001, -0.8660254037844386]}
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| Test Values: {-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]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.6.E4 17.6.E4] || [[Item:Q5371|<math>\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)</math>]] || <math>|cq| < |b^{2}|</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]])</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E5 17.6.E5] || [[Item:Q5372|<math>\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}}</math>]] || <math>|b| > |q|</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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}]}]]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E6 17.6.E6] || [[Item:Q5373|<math>\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}</math>]] || <math>|z| < 1, |b| < 1</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skip - No test values generated
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| | [https://dlmf.nist.gov/17.6.E7 17.6.E7] || [[Item:Q5374|<math>\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}</math>]] || <math>|z| < 1, |c| < |b|</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skip - No test values generated
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| | [https://dlmf.nist.gov/17.6.E8 17.6.E8] || [[Item:Q5375|<math>\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}}</math>]] || <math>|z| < 1, |abz| < |c|</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Missing Macro Error || Failure || - || Skip - No test values generated
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| | [https://dlmf.nist.gov/17.6.E9 17.6.E9] || [[Item:Q5376|<math>\qgenhyperphi{2}{1}@@{q,aq}{bq}{q}{z} = -\frac{(1-b)(aq/b)}{(1-(\ifrac{aq}{b}))}\sum_{n=0}^{\infty}\frac{\qmultiPochhammersym{aq,azq/b}{q}{n}q^{n}}{\qPochhammer{azq^{2}/b}{q}{n}}+\frac{\qmultiPochhammersym{aq,azq/b}{q}{\infty}}{\qPochhammer{aq/b}{q}{\infty}}\qgenhyperphi{2}{1}@@{q,0}{bq}{q}{z}</math>]] || <math>|z| < 1</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>QHypergeometricPFQ[{q , a*q},{b*q},q,z] == -Divide[(1 - b)*(a*q/b),1 -(Divide[a*q,b])]*Sum[Divide[Product[QPochhammer[Part[{a*q , a*z*q/b},i],q,n],{i,1,Length[{a*q , a*z*q/b}]}]*(q)^(n),QPochhammer[a*z*(q)^(2)/b, q, n]], {n, 0, Infinity}, GenerateConditions->None]+Divide[Product[QPochhammer[Part[{a*q , a*z*q/b},i],q,Infinity],{i,1,Length[{a*q , a*z*q/b}]}],QPochhammer[a*q/b, q, Infinity]]*QHypergeometricPFQ[{q , 0},{b*q},q,z]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E10 17.6.E10] || [[Item:Q5377|<math>(1-z)\qgenhyperphi{2}{1}@@{q,aq}{bq}{q}{z} = \sum_{n=0}^{\infty}\frac{\qPochhammer{b/a}{q}{n}(-az)^{n}q^{(n^{2}+n)/2}}{\qmultiPochhammersym{bq,zq}{q}{n}}</math>]] || <math>|z| < 1</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(1 - z)*QHypergeometricPFQ[{q , a*q},{b*q},q,z] == Sum[Divide[QPochhammer[b/a, q, n]*(- a*z)^(n)* (q)^(((n)^(2)+ n)/2),Product[QPochhammer[Part[{b*q , z*q},i],q,n],{i,1,Length[{b*q , z*q}]}]], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E11 17.6.E11] || [[Item:Q5378|<math>\frac{1-z}{1-b}\qgenhyperphi{2}{1}@@{q,aq}{bq}{q}{z} = \sum_{n=0}^{\infty}\frac{\qPochhammer{aq}{q}{n}\qPochhammer{azq/b}{q}{2n}b^{n}}{\qmultiPochhammersym{zq,aq/b}{q}{n}}-aq\sum_{n=0}^{\infty}\frac{\qPochhammer{aq}{q}{n}\qPochhammer{azq/b}{q}{2n+1}(bq)^{n}}{\qPochhammer{zq}{q}{n}\qPochhammer{aq/b}{q}{n+1}}</math>]] || <math>|z| < 1, |b| < 1</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[1 - z,1 - b]*QHypergeometricPFQ[{q , a*q},{b*q},q,z] == Sum[Divide[QPochhammer[a*q, q, n]*QPochhammer[a*z*q/b, q, 2*n]*(b)^(n),Product[QPochhammer[Part[{z*q , a*q/b},i],q,n],{i,1,Length[{z*q , a*q/b}]}]], {n, 0, Infinity}, GenerateConditions->None]- a*q*Sum[Divide[QPochhammer[a*q, q, n]*QPochhammer[a*z*q/b, q, 2*n + 1]*(b*q)^(n),QPochhammer[z*q, q, n]*QPochhammer[a*q/b, q, n + 1]], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E12 17.6.E12] || [[Item:Q5379|<math>(1-z)\qgenhyperphi{2}{1}@@{q,aq}{bq}{q}{z} = \sum_{n=0}^{\infty}\frac{\qmultiPochhammersym{aq,azq/b}{q}{n}}{\qmultiPochhammersym{bq,zq}{q}{n}}(1-azq^{2n+1})(bz)^{n}q^{n^{2}}</math>]] || <math>|z| < 1</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(1 - z)*QHypergeometricPFQ[{q , a*q},{b*q},q,z] == Sum[Divide[Product[QPochhammer[Part[{a*q , a*z*q/b},i],q,n],{i,1,Length[{a*q , a*z*q/b}]}],Product[QPochhammer[Part[{b*q , z*q},i],q,n],{i,1,Length[{b*q , z*q}]}]]*(1 - a*z*(q)^(2*n + 1))*(b*z)^(n)* (q)^((n)^(2)), {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E13 17.6.E13] || [[Item:Q5380|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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}]}]]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E14 17.6.E14] || [[Item:Q5381|<math>\sum_{n=0}^{\infty}\frac{\qPochhammer{a}{q}{n}\qPochhammer{b}{q^{2}}{n}z^{n}}{\qPochhammer{q}{q}{n}\qPochhammer{azb}{q^{2}}{n}} = \frac{\qmultiPochhammersym{az,bz}{q^{2}}{\infty}}{\qmultiPochhammersym{z,azb}{q^{2}}{\infty}}\qgenhyperphi{2}{1}@@{a,b}{bz}{q^{2}}{zq}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[QPochhammer[a, q, n]*QPochhammer[b, (q)^(2), n]*(z)^(n),QPochhammer[q, q, n]*QPochhammer[a*z*b, (q)^(2), n]], {n, 0, Infinity}, GenerateConditions->None] == Divide[Product[QPochhammer[Part[{a*z , b*z},i],(q)^(2),Infinity],{i,1,Length[{a*z , b*z}]}],Product[QPochhammer[Part[{z , a*z*b},i],(q)^(2),Infinity],{i,1,Length[{z , a*z*b}]}]]*QHypergeometricPFQ[{a , b},{b*z},(q)^(2),z*q]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E15 17.6.E15] || [[Item:Q5382|<math>\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}</math>]] || <math>|z| < 1, |bq| < |c|</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skip - No test values generated
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| | [https://dlmf.nist.gov/17.6.E16 17.6.E16] || [[Item:Q5383|<math>\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)}</math>]] || <math>|z| < 1, |abz| < |cq|</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E17 17.6.E17] || [[Item:Q5384|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E18 17.6.E18] || [[Item:Q5385|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E19 17.6.E19] || [[Item:Q5386|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E20 17.6.E20] || [[Item:Q5387|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E21 17.6.E21] || [[Item:Q5388|<math>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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E22 17.6.E22] || [[Item:Q5389|<math>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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E23 17.6.E23] || [[Item:Q5390|<math>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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E24 17.6.E24] || [[Item:Q5391|<math>(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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E25 17.6.E25] || [[Item:Q5392|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.6.E26 17.6.E26] || [[Item:Q5393|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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)]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [264 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[0.0, Times[Complex[0.8660254037844387, 0.49999999999999994], QHypergeometricPFQ[{-1.5, -1.5}
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| Test Values: {-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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 0.0], Times[Complex[0.5000000000000001, 0.8660254037844386], QHypergeometricPFQ[{-1.5, -1.5}
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| Test Values: {-1.5}, Complex[0.866025</div></div>
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| | [https://dlmf.nist.gov/17.6.E27 17.6.E27] || [[Item:Q5394|<math>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</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Times[Complex[9.528684177437189, -1.3259618943233384], QHypergeometricPFQ[{-1.5, -1.5}
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| Test Values: {-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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Times[Complex[5.290063509461103, -21.657849302036027], QHypergeometricPFQ[{-1.5, -1.5}
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| Test Values: {-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]]]}</syntax</div></div>
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| | [https://dlmf.nist.gov/17.6.E29 17.6.E29] || [[Item:Q5396|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.7.E1 17.7.E1] || [[Item:Q5397|<math>\qgenhyperphi{2}{2}@@{a,q/a}{-q,b}{q}{-b} = \frac{\qmultiPochhammersym{ab,bq/a}{q^{2}}{\infty}}{\qPochhammer{b}{q}{\infty}}</math>]] || <math>|b| < 1</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [96 / 120]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[QHypergeometricPFQ[{-1.5, Complex[-0.5773502691896257, -0.33333333333333326]}
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| Test Values: {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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[b, -0.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.7.E2 17.7.E2] || [[Item:Q5398|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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}]}]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[QHypergeometricPFQ[{2.25, 2.25}
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| Test Values: {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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Indeterminate
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| Test Values: {Rule[a, -1.5], Rule[b, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]</div></div>
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| | [https://dlmf.nist.gov/17.7.E3 17.7.E3] || [[Item:Q5399|<math>\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)}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]])</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [260 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[QHypergeometricPFQ[{1.0, 2.25}
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| Test Values: {-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</div></div>
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| | [https://dlmf.nist.gov/17.7.E4 17.7.E4] || [[Item:Q5400|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)}]}]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [196 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[0.0, QHypergeometricPFQ[{-1.5, -1.5, Complex[0.8660254037844387, -0.49999999999999994]}
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| Test Values: {-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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, -1.5, Complex[0.5000000000000001, -0.8660254037844386]}
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| Test Values: {-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]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.7.E5 17.7.E5] || [[Item:Q5401|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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}]}]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[0.0, QHypergeometricPFQ[{-1.5, -1.5, -1.5}
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| Test Values: {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[Co</div></div>
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| | [https://dlmf.nist.gov/17.7.E6 17.7.E6] || [[Item:Q5402|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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}]}]]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.7.E7 17.7.E7] || [[Item:Q5403|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)}]}]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [248 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[QHypergeometricPFQ[{-1.5, Complex[0.6123724356957944, -1.0606601717798212], -1.5, -1.5}
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| Test Values: {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[0.4082482904638</div></div>
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| | [https://dlmf.nist.gov/17.7.E8 17.7.E8] || [[Item:Q5404|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)}]}]]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.7.E11 17.7.E11] || [[Item:Q5407|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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}]}]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [296 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[0.0, QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], Complex[0.5000000000000001, 0.8660254037844386], -1.5, 1.5}
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| Test Values: {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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], Complex[0.0, 1.0], -1.5, 1.5}
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| Test Values: {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[Comp</div></div>
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| | [https://dlmf.nist.gov/17.7.E12 17.7.E12] || [[Item:Q5408|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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}]}]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [246 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[-1.299038105676658, -0.7499999999999999], Complex[1.1250000000000002, 1.9485571585149868], Complex[0.5000000000000001, -0.8660254037844386]}
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| Test Values: {-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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[-1.299038105676658, -0.7499999999999999], Complex[-1.1249999999999996, 1.948557158514987], Complex[-0.4999999999999998, -0.8660254037844387]}
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| Test Values: {-1.5, Complex[-1.299038105676658, -0.7499999999999999], Complex[1.1250000000000002, 1.9485571585149868]}, Complex[0.5000000000000001, 0.8660254037844386], Comple</div></div>
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| | [https://dlmf.nist.gov/17.7.E13 17.7.E13] || [[Item:Q5409|<math>\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})}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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))]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[-1.299038105676658, -0.7499999999999999], 2.25, Complex[0.5000000000000001, -0.8660254037844386]}
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| Test Values: {-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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[-1.299038105676658, -0.7499999999999999], Complex[1.1250000000000002, 1.9485571585149868], Complex[-0.4999999999999998, -0.8660254037844387]}
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| Test Values: {-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, Rationa</div></div>
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| | [https://dlmf.nist.gov/17.7.E16 17.7.E16] || [[Item:Q5412|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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}]}]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]}
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| Test Values: {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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[-46.07567037764495, -8.881784197001252*^-15], QHypergeometricPFQ[{-1.5, Complex[-0.6123724356957944, 1.0606601717798212], Complex[0.6123724356957944, -1.0606601717798212], -1.5, -1.5, </div></div>
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| | [https://dlmf.nist.gov/17.7.E20 17.7.E20] || [[Item:Q5416|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || Failure || Aborted || Error || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.7.E21 17.7.E21] || [[Item:Q5417|<math>\sum_{k=0}^{n}\frac{(1-ap^{k}q^{k})(1-bp^{k}q^{-k})}{(1-a)(1-b)}\frac{\qmultiPochhammersym{a,b}{p}{k}\qmultiPochhammersym{c,a/(bc)}{q}{k}}{\qmultiPochhammersym{q,aq/b}{q}{k}\qmultiPochhammersym{ap/c,bcp}{p}{k}}q^{k} = \frac{\qmultiPochhammersym{ap,bp}{p}{n}\qmultiPochhammersym{cq,aq/(bc)}{q}{n}}{\qmultiPochhammersym{q,aq/b}{q}{n}\qmultiPochhammersym{ap/c,bcp}{p}{n}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[(1 - a*(p)^(k)* (q)^(k))*(1 - b*(p)^(k)* (q)^(- k)),(1 - a)*(1 - b)]*Divide[Product[QPochhammer[Part[{a , b},i],p,k],{i,1,Length[{a , b}]}]*Product[QPochhammer[Part[{c , a/(b*c)},i],q,k],{i,1,Length[{c , a/(b*c)}]}],Product[QPochhammer[Part[{q , a*q/b},i],q,k],{i,1,Length[{q , a*q/b}]}]*Product[QPochhammer[Part[{a*p/c , b*c*p},i],p,k],{i,1,Length[{a*p/c , b*c*p}]}]]*(q)^(k), {k, 0, n}, GenerateConditions->None] == Divide[Product[QPochhammer[Part[{a*p , b*p},i],p,n],{i,1,Length[{a*p , b*p}]}]*Product[QPochhammer[Part[{c*q , a*q/(b*c)},i],q,n],{i,1,Length[{c*q , a*q/(b*c)}]}],Product[QPochhammer[Part[{q , a*q/b},i],q,n],{i,1,Length[{q , a*q/b}]}]*Product[QPochhammer[Part[{a*p/c , b*c*p},i],p,n],{i,1,Length[{a*p/c , b*c*p}]}]]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.7.E22 17.7.E22] || [[Item:Q5418|<math>\sum_{k=-m}^{n}\frac{(1-adp^{k}q^{k})(1-bp^{k}/(dq^{k}))}{(1-ad)(1-(b/d))}\frac{\qmultiPochhammersym{a,b}{p}{k}\qmultiPochhammersym{c,ad^{2}/(bc)}{q}{k}}{\qmultiPochhammersym{dq,adq/b}{q}{k}\qmultiPochhammersym{adp/c,bcp/d}{p}{k}}q^{k} = \frac{(1-a)(1-b)(1-c)(1-(ad^{2}/(bc)))}{d(1-ad)(1-(b/d))(1-(c/d))(1-(ad/(bc)))}\left(\frac{\qmultiPochhammersym{ap,bp}{p}{n}\qmultiPochhammersym{cq,ad^{2}q/(bc)}{q}{n}}{\qmultiPochhammersym{dq,adq/b}{q}{n}\qmultiPochhammersym{adp/c,bcp/d}{p}{n}}-\frac{\qmultiPochhammersym{c/(ad),d/(bc)}{p}{m+1}\qmultiPochhammersym{1/d,b/(ad)}{q}{m+1}}{\qmultiPochhammersym{1/c,bc/(ad^{2})}{q}{m+1}\qmultiPochhammersym{1/a,1/b}{p}{m+1}}\right)</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[(1 - a*d*(p)^(k)* (q)^(k))*(1 - b*(p)^(k)/(d*(q)^(k))),(1 - a*d)*(1 -(b/d))]*Divide[Product[QPochhammer[Part[{a , b},i],p,k],{i,1,Length[{a , b}]}]*Product[QPochhammer[Part[{c , a*(d)^(2)/(b*c)},i],q,k],{i,1,Length[{c , a*(d)^(2)/(b*c)}]}],Product[QPochhammer[Part[{d*q , a*d*q/b},i],q,k],{i,1,Length[{d*q , a*d*q/b}]}]*Product[QPochhammer[Part[{a*d*p/c , b*c*p/d},i],p,k],{i,1,Length[{a*d*p/c , b*c*p/d}]}]]*(q)^(k), {k, - m, n}, GenerateConditions->None] == Divide[(1 - a)*(1 - b)*(1 - c)*(1 -(a*(d)^(2)/(b*c))),d*(1 - a*d)*(1 -(b/d))*(1 -(c/d))*(1 -(a*d/(b*c)))]*(Divide[Product[QPochhammer[Part[{a*p , b*p},i],p,n],{i,1,Length[{a*p , b*p}]}]*Product[QPochhammer[Part[{c*q , a*(d)^(2)* q/(b*c)},i],q,n],{i,1,Length[{c*q , a*(d)^(2)* q/(b*c)}]}],Product[QPochhammer[Part[{d*q , a*d*q/b},i],q,n],{i,1,Length[{d*q , a*d*q/b}]}]*Product[QPochhammer[Part[{a*d*p/c , b*c*p/d},i],p,n],{i,1,Length[{a*d*p/c , b*c*p/d}]}]]-Divide[Product[QPochhammer[Part[{c/(a*d), d/(b*c)},i],p,m + 1],{i,1,Length[{c/(a*d), d/(b*c)}]}]*Product[QPochhammer[Part[{1/d , b/(a*d)},i],q,m + 1],{i,1,Length[{1/d , b/(a*d)}]}],Product[QPochhammer[Part[{1/c , b*c/(a*(d)^(2))},i],q,m + 1],{i,1,Length[{1/c , b*c/(a*(d)^(2))}]}]*Product[QPochhammer[Part[{1/a , 1/b},i],p,m + 1],{i,1,Length[{1/a , 1/b}]}]])</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.7.E23 17.7.E23] || [[Item:Q5419|<math>\left(1-\frac{a}{q}\right)\left(1-\frac{b}{q}\right)\sum_{k=0}^{n}\frac{\qmultiPochhammersym{ap^{k},bp^{-k}}{q}{n-1}(1-(ap^{2k}/b))}{\qPochhammer{p}{p}{n}\qPochhammer{p}{p}{n-k}\qPochhammer{ap^{k}/b}{q}{n+1}}(-1)^{k}p^{\binom{k}{2}} = \Kroneckerdelta{n}{0}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(1 -Divide[a,q])*(1 -Divide[b,q])*Sum[Divide[Product[QPochhammer[Part[{a*(p)^(k), b*(p)^(- k)},i],q,n - 1],{i,1,Length[{a*(p)^(k), b*(p)^(- k)}]}]*(1 -(a*(p)^(2*k)/b)),QPochhammer[p, p, n]*QPochhammer[p, p, n - k]*QPochhammer[a*(p)^(k)/b, q, n + 1]]*(- 1)^(k)* (p)^(Binomial[k,2]), {k, 0, n}, GenerateConditions->None] == KroneckerDelta[n, 0]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.8.E1 17.8.E1] || [[Item:Q5420|<math>\sum_{n=-\infty}^{\infty}(-z)^{n}q^{n(n-1)/2} = \qmultiPochhammersym{q,z,q/z}{q}{\infty}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(- z)^(n)* (q)^(n*(n - 1)/2), {n, - Infinity, Infinity}, GenerateConditions->None] == Product[QPochhammer[Part[{q , z , q/z},i],q,Infinity],{i,1,Length[{q , z , q/z}]}]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.8.E3 17.8.E3] || [[Item:Q5422|<math>\sum_{n=-\infty}^{\infty}(-1)^{n}q^{n(3n-1)/2}z^{3n}(1+zq^{n}) = \qmultiPochhammersym{q,-z,-q/z}{q}{\infty}\qmultiPochhammersym{qz^{2},q/{z^{2}}}{q^{2}}{\infty}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(- 1)^(n)* (q)^(n*(3*n - 1)/2)* (z)^(3*n)*(1 + z*(q)^(n)), {n, - Infinity, Infinity}, GenerateConditions->None] == Product[QPochhammer[Part[{q , - z , - q/z},i],q,Infinity],{i,1,Length[{q , - z , - q/z}]}]*Product[QPochhammer[Part[{q*(z)^(2), q/(z)^(2)},i],(q)^(2),Infinity],{i,1,Length[{q*(z)^(2), q/(z)^(2)}]}]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.9.E1 17.9.E1] || [[Item:Q5427|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.9.E2 17.9.E2] || [[Item:Q5428|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [290 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[0.0, QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5}
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| Test Values: {-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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5}
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| Test Values: {-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]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.9.E3 17.9.E3] || [[Item:Q5429|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.9.E4 17.9.E4] || [[Item:Q5430|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [294 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5}
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| Test Values: {-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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5}
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| Test Values: {-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]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.9.E5 17.9.E5] || [[Item:Q5431|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [294 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[0.0, QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5}
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| Test Values: {-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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5}
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| Test Values: {-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]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.9.E6 17.9.E6] || [[Item:Q5432|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [264 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[QHypergeometricPFQ[{-1.5, -1.5, -1.5}
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| Test Values: {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], Co</div></div>
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| | [https://dlmf.nist.gov/17.9.E7 17.9.E7] || [[Item:Q5433|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[QHypergeometricPFQ[{-1.5, -1.5, -1.5}
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| Test Values: {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, 0.49999999999</div></div>
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| | [https://dlmf.nist.gov/17.9.E8 17.9.E8] || [[Item:Q5434|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [188 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, -1.5}
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| Test Values: {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]]]}<</div></div>
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| | [https://dlmf.nist.gov/17.9.E9 17.9.E9] || [[Item:Q5435|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [228 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, -1.5}
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| Test Values: {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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[QHypergeome</div></div>
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| | [https://dlmf.nist.gov/17.9.E10 17.9.E10] || [[Item:Q5436|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [198 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, -1.5}
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| Test Values: {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]]]}</syntaxhighlight><br><syntaxhighlight lan</div></div>
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| | [https://dlmf.nist.gov/17.9.E11 17.9.E11] || [[Item:Q5437|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, -1.5}
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| Test Values: {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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathema</div></div>
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| | [https://dlmf.nist.gov/17.9.E12 17.9.E12] || [[Item:Q5438|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [246 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[0.0, QHypergeometricPFQ[{-1.5, -1.5, -1.5}
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| Test Values: {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[0.8660254</div></div>
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| | [https://dlmf.nist.gov/17.9.E13 17.9.E13] || [[Item:Q5439|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [246 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[QHypergeometricPFQ[{-1.5, -1.5, -1.5}
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| Test Values: {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[</div></div>
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| | [https://dlmf.nist.gov/17.9.E14 17.9.E14] || [[Item:Q5440|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.9.E14 17.9.E14] || [[Item:Q5440|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.9.E15 17.9.E15] || [[Item:Q5441|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]}
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| Test Values: {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, 0.49</div></div>
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| | [https://dlmf.nist.gov/17.9.E16 17.9.E16] || [[Item:Q5442|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.9.E17 17.9.E17] || [[Item:Q5443|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [298 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[QHypergeometricPFQ[{-1.5, -1.5, -1.5}
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| Test Values: {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, 0.499</div></div>
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| | [https://dlmf.nist.gov/17.9.E18 17.9.E18] || [[Item:Q5444|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>(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]</syntaxhighlight> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [284 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Power[QHypergeometricPFQ[{-1.5, -1.5, Complex[1.948557158514987, 1.1249999999999998], Complex[1.948557158514987, -1.1249999999999998]}
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| Test Values: {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]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Plus[Power[QHyper</div></div>
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| | [https://dlmf.nist.gov/17.9.E19 17.9.E19] || [[Item:Q5445|<math>\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}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Aborted || Error || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.9.E20 17.9.E20] || [[Item:Q5446|<math>\sum_{n=0}^{\infty}\frac{\qPochhammer{a}{q^{k}}{n}\qPochhammer{b}{q}{kn}z^{n}}{\qPochhammer{q^{k}}{q^{k}}{n}\qPochhammer{c}{q}{kn}} = \frac{\qPochhammer{b}{q}{\infty}\qPochhammer{az}{q^{k}}{\infty}}{\qPochhammer{c}{q}{\infty}\qPochhammer{z}{q^{k}}{\infty}}\sum_{n=0}^{\infty}\frac{\qPochhammer{c/b}{q}{n}\qPochhammer{z}{q^{k}}{n}b^{n}}{\qPochhammer{q}{q}{n}\qPochhammer{az}{q^{k}}{n}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum((QPochhammer(a, (q)^(k), n)*QPochhammer(b, q, k*n)*(z)^(n))/(QPochhammer((q)^(k), (q)^(k), n)*QPochhammer(c, q, k*n)), n = 0..infinity) = (QPochhammer(b, q, infinity)*QPochhammer(a*z, (q)^(k), infinity))/(QPochhammer(c, q, infinity)*QPochhammer(z, (q)^(k), infinity))*sum((QPochhammer(c/b, q, n)*QPochhammer(z, (q)^(k), n)*(b)^(n))/(QPochhammer(q, q, n)*QPochhammer(a*z, (q)^(k), n)), n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Divide[QPochhammer[a, (q)^(k), n]*QPochhammer[b, q, k*n]*(z)^(n),QPochhammer[(q)^(k), (q)^(k), n]*QPochhammer[c, q, k*n]], {n, 0, Infinity}, GenerateConditions->None] == Divide[QPochhammer[b, q, Infinity]*QPochhammer[a*z, (q)^(k), Infinity],QPochhammer[c, q, Infinity]*QPochhammer[z, (q)^(k), Infinity]]*Sum[Divide[QPochhammer[c/b, q, n]*QPochhammer[z, (q)^(k), n]*(b)^(n),QPochhammer[q, q, n]*QPochhammer[a*z, (q)^(k), n]], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Error || Aborted || - || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.12.E1 17.12.E1] || [[Item:Q5457|<math>\sum_{n=0}^{\infty}\alpha_{n}\gamma_{n} = \sum_{n=0}^{\infty}\beta_{n}\delta_{n}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>sum(alpha[n]*gamma[n], n = 0..infinity) = sum(beta[n]*delta[n], n = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Subscript[\[Alpha], n]*Subscript[\[Gamma], n], {n, 0, Infinity}, GenerateConditions->None] == Sum[Subscript[\[Beta], n]*Subscript[\[Delta], n], {n, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| | [https://dlmf.nist.gov/17.12#Ex1 17.12#Ex1] || [[Item:Q5458|<math>\beta_{n} = \sum_{j=0}^{n}\alpha_{j}u_{n-j}v_{n+j}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>beta[n] = sum(alpha[j]*u[n - j]*v[n + j], j = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[\[Beta], n] == Sum[Subscript[\[Alpha], j]*Subscript[u, n - j]*Subscript[v, n + j], {j, 0, n}, GenerateConditions->None]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| | [https://dlmf.nist.gov/17.12#Ex2 17.12#Ex2] || [[Item:Q5459|<math>\gamma_{n} = \sum_{j=n}^{\infty}\delta_{j}u_{j-n}v_{j+n}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>gamma[n] = sum(delta[j]*u[j - n]*v[j + n], j = n..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[\[Gamma], n] == Sum[Subscript[\[Delta], j]*Subscript[u, j - n]*Subscript[v, j + n], {j, n, Infinity}, GenerateConditions->None]</syntaxhighlight> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| | [https://dlmf.nist.gov/17.12.E3 17.12.E3] || [[Item:Q5460|<math>\beta_{n} = \sum_{j=0}^{n}\frac{\alpha_{j}}{\qPochhammer{q}{q}{n-j}\qPochhammer{aq}{q}{n+j}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>beta[n] = sum((alpha[j])/(QPochhammer(q, q, n - j)*QPochhammer(a*q, q, n + j)), j = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[\[Beta], n] == Sum[Divide[Subscript[\[Alpha], j],QPochhammer[q, q, n - j]*QPochhammer[a*q, q, n + j]], {j, 0, n}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.6508376433032488, -0.21856268949920582]
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| Test Values: {Rule[a, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[Subscript[α, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[β, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.8660402331469415, 0.20457300495175623]
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| Test Values: {Rule[a, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[Subscript[α, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[β, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.12.E4 17.12.E4] || [[Item:Q5461|<math>\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}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>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)</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]</syntaxhighlight> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out
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| | [https://dlmf.nist.gov/17.12#Ex5 17.12#Ex5] || [[Item:Q5464|<math>\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)}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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)]</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[5.814582562299427, -3.4240381056766607]
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| Test Values: {Rule[a, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[α, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-12.010896071760529, -4.7481964481437355]
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| Test Values: {Rule[a, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[α, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.12#Ex6 17.12#Ex6] || [[Item:Q5465|<math>\beta_{n} = \frac{1}{\qPochhammer{q}{q}{n}}</math>]] || <math></math> || <syntaxhighlight lang=mathematica>beta[n] = (1)/(QPochhammer(q, q, n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[\[Beta], n] == Divide[1,QPochhammer[q, q, n]]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [297 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.3660254037844387, -1.366025403784439]
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| Test Values: {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[β, 1.5], Rule[Subscript[β, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[2.232050807568878, -0.8660254037844388]
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| Test Values: {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[β, 1.5], Rule[Subscript[β, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| | [https://dlmf.nist.gov/17.13.E3 17.13.E3] || [[Item:Q5468|<math>\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}}</math>]] || <math>\realpart@@{\alpha} > 0, \realpart@@{1-\alpha} > 0</math> || <syntaxhighlight lang=mathematica>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))</syntaxhighlight> || <syntaxhighlight lang=mathematica>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]]</syntaxhighlight> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [26 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 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]]]
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| Test Values: {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]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 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]</div></div>
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| |}
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