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| ! DLMF !! Formula !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica | | ! DLMF !! Formula !! Maple !! Mathematica !! Symbolic<br>Maple !! Symbolic<br>Mathematica !! Numeric<br>Maple !! Numeric<br>Mathematica |
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| | [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>]] || <code> QPochhammer(a, q, - n) = ( 1)/( QPochhammer(a *( q)^( - n) , q, n))</code> || <code> QPochhammer[a, q, - n] == Divide[ 1,QPochhammer[a*( q)^(- n) , q, n]]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 18 / 180]<div class="mw-collapsible-content"><code>{ Indeterminate <- {Rule[a, -1.5], Rule[ n, 1], Rule[q, -1 .5]}</code><br><code> Indeterminate <- {Rule[a, -1.5], Rule[ n, 2], Rule[q, -1 .5]}</code><br></div></div> | | | [https://dlmf.nist.gov/ 16.2. E3 16.2. E3] || [[Item: Q5185|<math>\ genhyperF{ p+1}{q} @@{- m,\mathbf{a}}{\mathbf{b}}{z} = \frac{ \Pochhammersym{\mathbf{a}}{m}(-z)^{m}}{\Pochhammersym{\mathbf{b}}{m}}\genhyperF{q+1}{ p}@@{-m,1-m-\ mathbf{ b}}{ 1-m- \mathbf{a}}{ \frac{(-1)^{p+q }}{ z}}</math>]] || <code> hypergeom( [- m , a ], [b], z) = (pochhammer(a, m)*(- z) ^( m))/( pochhammer(b, m))*hypergeom( [- m , 1 - m - b], [1 - m - a ], (( - 1)^( p + q)) /(z))</code> || <code> HypergeometricPFQ[ {- m , a }, {b}, z] == Divide[ Pochhammer[a , m]*( - z)^( m),Pochhammer[b, m]]*HypergeometricPFQ[{- m , 1 - m - b}, {1 - m - a}, Divide[(- 1) ^(p + q ), z]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [258 / 300]<div class="mw-collapsible-content"><code>258/300]: [[.9712138727+.322304453e-1*I <- {a = -3/2, b = -3/2, p = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}</code><br><code>-.6497511671-1.025183062*I <- {a = - 3/2, b = -3/2, p = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 258 / 300]<div class="mw-collapsible-content"><code>{ Complex[0.9712138727144691, 0.032230445352325054] <- {Rule[a, -1.5], Rule[ b, -1.5], Rule[m, 1], Rule[p, Power[E, Times[Complex[0, Rational[1 , 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1 , 6]], Pi]]]}</code><br><code> Complex[-0.6497511667213578, -1.0251830622105054] <- {Rule[a, -1.5], Rule[ b, -1.5], Rule[m, 2 ], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1 , 6]], Pi]]]}</code><br></div></div> |
| |- | | |- |
| | [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>]] || <code>( 1)/( QPochhammer( a*( q)^( - n), q, n)) = (( - q/ a)^( n) * (q) ^( binomial( n, 2))) /( QPochhammer(q/ a, q, n))</code> || <code>Divide[ 1, QPochhammer[ a*( q)^( - n), q, n]] == Divide[( - q/ a)^( n)* ( q) ^(Binomial[ n, 2]), QPochhammer[q/ a, q, n]]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 18 / 180]<div class="mw-collapsible-content"><code>{ Indeterminate <- {Rule[a, -1.5], Rule[ n, 1], Rule[q, -1 .5]}</code><br><code> Indeterminate <- {Rule[a, -1.5], Rule[ n, 2], Rule[q, -1 .5]}</code><br></div></div> | | | [https://dlmf.nist.gov/ 16.2. E4 16.2. E4] || [[Item: Q5186|<math> \sum_{k=0}^{m}\frac{ \Pochhammersym{\mathbf{a}}{k}}{\ Pochhammersym{ \mathbf{ b}}{ k}} \frac{z^{ k}} {k!} = \frac{ \Pochhammersym{\mathbf{a }}{m}z^{ m} }{\Pochhammersym{\ mathbf{ b}}{ m}m!}\genhyperF{q+2} {p}@@{-m,1,1-m-\mathbf{b}}{ 1-m-\ mathbf{a }}{ \frac{(-1)^{p+q +1}}{ z}}</math>]] || <code> sum( (pochhammer(a, k))/( pochhammer( b, k))*( (z)^( k))/(factorial(k)), k = 0..m) = ( pochhammer(a , m)*(z)^( m)) /( pochhammer( b, m) *factorial(m)) *hypergeom([- m , 1 , 1 - m - b], [1 - m - a], (( - 1)^( p + q + 1))/ (z))</code> || <code> Sum[Divide[ Pochhammer[a, k], Pochhammer[ b, k]]* Divide[( z)^( k),(k) !], {k, 0, m}, GenerateConditions->None] == Divide[ Pochhammer[a, m]*( z)^( m) ,Pochhammer[b, m]*( m) !]*HypergeometricPFQ[ {- m , 1 , 1 - m - b}, {1 - m - a }, Divide[(- 1)^(p + q + 1), z]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [258 / 300]<div class="mw-collapsible-content"><code>258/300]: [[.9712138726+.322304451e-1*I <- {a = -3/2, b = - 3/2, p = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 1}</code><br><code>1.825190824+.5153748995*I <- {a = -3/2, b = -3/2, p = 1/2*3^(1/2)+1/2*I, q = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I, m = 2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 258 / 300]<div class="mw-collapsible-content"><code>{ Complex[0.9712138727144698, 0.03223044535232533] <- {Rule[a, -1.5], Rule[ b, -1.5], Rule[m, 1], Rule[p, Power[E, Times[Complex[0, Rational[1 , 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1 , 6]], Pi]]]}</code><br><code> Complex[1.8251908240859445, 0.5153749002123968] <- {Rule[a, -1.5], Rule[ b, -1.5], Rule[m, 2 ], Rule[p, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1 , 6]], Pi]]]}</code><br></div></div> |
| |- | | |- |
| | [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>]] || <code> QPochhammer( a, q, nu) = product((1 - a*( q)^( j) )/( 1 - a*( q)^( nu + j)) , j = 0..infinity)</code> || <code> QPochhammer[ a, q, \[Nu]] == Product[Divide[1 - a*( q)^( j) ,1 - a*( q)^( \[Nu]+ j) ], { j, 0, Infinity} , GenerateConditions->None]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 33 / 300]<div class="mw-collapsible-content"><code>{ Indeterminate <- { Rule[a, -1 .5], Rule[q, Power[E, Times[Complex[0, Rational[2 , 3]], Pi]]], Rule[ ν, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code> Indeterminate <- {Rule[ a, - 1. 5] , Rule[ q, Power[E, Times[Complex[0, Rational[2, 3 ]], Pi]]], Rule[ ν, Power[E, Times[Complex[0, Rational[ 2, 3]], Pi]]]}</code><br></div></div> | | | [https://dlmf.nist.gov/ 16. 3. E5 16. 3. E5] || [[Item: Q5192|<math>\ left(z\deriv{}{ z} z\right)^{ n} = z^{ n}\ deriv[n]{ }{ z} z^{ n}</math>]] || <code>( z*diff(z, z))^(n) = ( z)^( n) * diff(( z)^( n) , [z$(n) ])</code> || <code> (z*D[ z, z] )^(n) == ( z)^( n)* D[( z)^( n), { z, n}]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 7 / 7]<div class="mw-collapsible-content"><code> 7/7]: [[-.1616869430e-8-5.000000005*I <- { z = 1/2*3^(1/2)+1/2*I, n = 3}</code><br><code>-5.000000005+.1616869430e-8*I <- { z = -1 /2+1/2*I*3^(1/2), n = 3}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 14 / 21]<div class="mw-collapsible-content"><code>{Complex[ -0 .5000000000000001, -0.8660254037844386] <- {Rule[ n, 2], Rule[ z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code> Complex[ 0.0, - 5. 0] <- {Rule[ n, 3], Rule[ z, Power[E, Times[Complex[0, Rational[ 1, 6]], Pi]]]}</code><br></div></div> |
| |- | | |- |
| | [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>]] || <code>QPochhammer(a, q, infinity) = product(1 - a*(q)^(j), j = 0..infinity)</code> || <code>QPochhammer[a, q, Infinity] == Product[1 - a*(q)^(j), {j, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [48 / 60]<div class="mw-collapsible-content"><code>{Plus[Times[-1.0, QPochhammer[-1.5, Complex[0.8660254037844387, 0.49999999999999994]]], QPochhammer[-1.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]] <- {Rule[a, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Indeterminate <- {Rule[a, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div> | | | [https://dlmf.nist.gov/16.3.E6 16.3.E6] || [[Item:Q5193|<math>z\genhyperF{0}{1}@{-}{b+1}{z}+b(b-1)\genhyperF{0}{1}@{-}{b}{z}-b(b-1)\genhyperF{0}{1}@{-}{b-1}{z} = 0</math>]] || <code>z*hypergeom([-], [b + 1], z)+ b*(b - 1)* hypergeom([-], [b], z)- b*(b - 1)* hypergeom([-], [b - 1], z) = 0</code> || <code>z*HypergeometricPFQ[{-}, {b + 1}, z]+ b*(b - 1)* HypergeometricPFQ[{-}, {b}, z]- b*(b - 1)* HypergeometricPFQ[{-}, {b - 1}, z] == 0</code> || Error || Failure || - || Error |
| |- | | |- |
| | [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>]] || <code>QPochhammer(a, (q)^(- 1), n) = QPochhammer((a)^(- 1), q, n)*(- a)^(n)* (q)^(-binomial(n,2))</code> || <code>QPochhammer[a, (q)^(- 1), n] == QPochhammer[(a)^(- 1), q, n]*(- a)^(n)* (q)^(-Binomial[n,2])</code> || Successful || Failure || - || Successful [Tested: 180] | | | [https://dlmf.nist.gov/16.3.E7 16.3.E7] || [[Item:Q5194|<math>\genhyperF{3}{2}@@{a_{1}+2,a_{2},a_{3}}{b_{1},b_{2}}{z}a_{1}(a_{1}+1)(1-z)+\genhyperF{3}{2}@@{a_{1}+1,a_{2},a_{3}}{b_{1},b_{2}}{z}a_{1}\left(b_{1}+b_{2}-3a_{1}-2+z(2a_{1}-a_{2}-a_{3}+1)\right)+\genhyperF{3}{2}@@{a_{1},a_{2},a_{3}}{b_{1},b_{2}}{z}\left((2a_{1}-b_{1})(2a_{1}-b_{2})+a_{1}-a_{1}^{2}-z(a_{1}-a_{2})(a_{1}-a_{3})\right)-\genhyperF{3}{2}@@{a_{1}-1,a_{2},a_{3}}{b_{1},b_{2}}{z}(a_{1}-b_{1})(a_{1}-b_{2}) = 0</math>]] || <code>hypergeom([a[1]+ 2 , a[2], a[3]], [b[1], b[2]], z)*a[1]*(a[1]+ 1)*(1 - z)+ hypergeom([a[1]+ 1 , a[2], a[3]], [b[1], b[2]], z)*a[1]*(b[1]+ b[2]- 3*a[1]- 2 + z*(2*a[1]- a[2]- a[3]+ 1))+ ((2*a[1]- b[1])*(2*a[1]- b[2])+ a[1]- a(a[1])^(2)- z*(a[1]- a[2])*(a[1]- a[3]))- hypergeom([a[1]- 1 , a[2], a[3]], [b[1], b[2]], z)*(a[1]- b[1])*(a[1]- b[2]) = 0</code> || <code>HypergeometricPFQ[{Subscript[a, 1]+ 2 , Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z]*Subscript[a, 1]*(Subscript[a, 1]+ 1)*(1 - z)+ HypergeometricPFQ[{Subscript[a, 1]+ 1 , Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z]*Subscript[a, 1]*(Subscript[b, 1]+ Subscript[b, 2]- 3*Subscript[a, 1]- 2 + z*(2*Subscript[a, 1]- Subscript[a, 2]- Subscript[a, 3]+ 1))+ ((2*Subscript[a, 1]- Subscript[b, 1])*(2*Subscript[a, 1]- Subscript[b, 2])+ Subscript[a, 1]- a(Subscript[a, 1])^(2)- z*(Subscript[a, 1]- Subscript[a, 2])*(Subscript[a, 1]- Subscript[a, 3]))- HypergeometricPFQ[{Subscript[a, 1]- 1 , Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, z]*(Subscript[a, 1]- Subscript[b, 1])*(Subscript[a, 1]- Subscript[b, 2]) == 0</code> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[1.7372028395654344, 0.5250871122698257], Times[Complex[-0.5000000000000001, -0.8660254037844386], a]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[4.427028162877593, -11.419461015230842], Times[Complex[-0.5000000000000001, -0.8660254037844386], a]] <- {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, 1], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, 2], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[a, 3], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[b, 1], Power[E, Times[Complex[0,</div></div> |
| |- | | |- |
| | [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>]] || <code>(QPochhammer(a, (q)^(- 1), n))/(QPochhammer(b, (q)^(- 1), n)) = (QPochhammer((a)^(- 1), q, n))/(QPochhammer((b)^(- 1), q, n))*((a)/(b))^(n)</code> || <code>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)</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [20 / 300]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[q, -1.5]}</code><br><code>Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 3], Rule[q, -1.5]}</code><br></div></div> | | | [https://dlmf.nist.gov/16.4.E1 16.4.E1] || [[Item:Q5195|<math>a_{q}+b_{q} = a_{q+1}+1</math>]] || <code>a[q]+ b[q] = a[q + 1]+ 1</code> || <code>Subscript[a, q]+ Subscript[b, q] == Subscript[a, q + 1]+ 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || - |
| |- | | |- |
| | [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>]] || <code>QPochhammer(a, q, n) = QPochhammer((q)^(1 - n)/ a, q, n)*(- a)^(n)* (q)^(binomial(n,2))</code> || <code>QPochhammer[a, q, n] == QPochhammer[(q)^(1 - n)/ a, q, n]*(- a)^(n)* (q)^(Binomial[n,2])</code> || Successful || Failure || - || Successful [Tested: 180] | | | [https://dlmf.nist.gov/16.4.E3 16.4.E3] || [[Item:Q5197|<math>\genhyperF{3}{2}@@{-n,a,b}{c,d}{1} = \frac{\Pochhammersym{c-a}{n}\Pochhammersym{c-b}{n}}{\Pochhammersym{c}{n}\Pochhammersym{c-a-b}{n}}</math>]] || <code>hypergeom([- n , a , b], [c , d], 1) = (pochhammer(c - a, n)*pochhammer(c - b, n))/(pochhammer(c, n)*pochhammer(c - a - b, n))</code> || <code>HypergeometricPFQ[{- n , a , b}, {c , d}, 1] == Divide[Pochhammer[c - a, n]*Pochhammer[c - b, n],Pochhammer[c, n]*Pochhammer[c - a - b, n]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [281 / 300]<div class="mw-collapsible-content"><code>281/300]: [[2.299038106-.7499999997*I <- {a = -3/2, b = -3/2, c = -3/2, d = 1/2*3^(1/2)+1/2*I, n = 1}</code><br><code>3.872595264-1.774519052*I <- {a = -3/2, b = -3/2, c = -3/2, d = 1/2*3^(1/2)+1/2*I, n = 2}</code><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [281 / 300]<div class="mw-collapsible-content"><code>{Complex[2.299038105676658, -0.7499999999999998] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1]}</code><br><code>Complex[3.872595264191645, -1.7745190528383286] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2]}</code><br></div></div> |
| |- | | |- |
| | [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>]] || <code>(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)</code> || <code>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)</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [12 / 300]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[a, -1.5], Rule[b, -0.5], Rule[n, 2], Rule[q, -2]}</code><br><code>Indeterminate <- {Rule[a, -1.5], Rule[b, -0.5], Rule[n, 3], Rule[q, -2]}</code><br></div></div> | | | [https://dlmf.nist.gov/16.4.E4 16.4.E4] || [[Item:Q5198|<math>\genhyperF{3}{2}@@{a,b,c}{a-b+1,a-c+1}{1} = \frac{\EulerGamma@{\frac{1}{2}a+1}\EulerGamma@{a-b+1}\EulerGamma@{a-c+1}\EulerGamma@{\frac{1}{2}a-b-c+1}}{\EulerGamma@{a+1}\EulerGamma@{\frac{1}{2}a-b+1}\EulerGamma@{\frac{1}{2}a-c+1}\EulerGamma@{a-b-c+1}}</math>]] || <code>hypergeom([a , b , c], [a - b + 1 , a - c + 1], 1) = (GAMMA((1)/(2)*a + 1)*GAMMA(a - b + 1)*GAMMA(a - c + 1)*GAMMA((1)/(2)*a - b - c + 1))/(GAMMA(a + 1)*GAMMA((1)/(2)*a - b + 1)*GAMMA((1)/(2)*a - c + 1)*GAMMA(a - b - c + 1))</code> || <code>HypergeometricPFQ[{a , b , c}, {a - b + 1 , a - c + 1}, 1] == Divide[Gamma[Divide[1,2]*a + 1]*Gamma[a - b + 1]*Gamma[a - c + 1]*Gamma[Divide[1,2]*a - b - c + 1],Gamma[a + 1]*Gamma[Divide[1,2]*a - b + 1]*Gamma[Divide[1,2]*a - c + 1]*Gamma[a - b - c + 1]]</code> || Successful || Successful || - || Successful [Tested: 69] |
| |- | | |- |
| | [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>]] || <code>QPochhammer(a*(q)^(- n), q, n) = QPochhammer(q/ a, q, n)*(-(a)/(q))^(n)* (q)^(-binomial(n,2))</code> || <code>QPochhammer[a*(q)^(- n), q, n] == QPochhammer[q/ a, q, n]*(-Divide[a,q])^(n)* (q)^(-Binomial[n,2])</code> || Successful || Failure || - || Successful [Tested: 180] | | | [https://dlmf.nist.gov/16.4.E6 16.4.E6] || [[Item:Q5200|<math>\genhyperF{3}{2}@@{a,b,c}{\frac{1}{2}(a+b+1),2c}{1} = \frac{\EulerGamma@{\frac{1}{2}}\EulerGamma@{c+\frac{1}{2}}\EulerGamma@{\frac{1}{2}(a+b+1)}\EulerGamma@{c+\frac{1}{2}(1-a-b)}}{\EulerGamma@{\frac{1}{2}(a+1)}\EulerGamma@{\frac{1}{2}(b+1)}\EulerGamma@{c+\frac{1}{2}(1-a)}\EulerGamma@{c+\frac{1}{2}(1-b)}}</math>]] || <code>hypergeom([a , b , c], [(1)/(2)*(a + b + 1), 2*c], 1) = (GAMMA((1)/(2))*GAMMA(c +(1)/(2))*GAMMA((1)/(2)*(a + b + 1))*GAMMA(c +(1)/(2)*(1 - a - b)))/(GAMMA((1)/(2)*(a + 1))*GAMMA((1)/(2)*(b + 1))*GAMMA(c +(1)/(2)*(1 - a))*GAMMA(c +(1)/(2)*(1 - b)))</code> || <code>HypergeometricPFQ[{a , b , c}, {Divide[1,2]*(a + b + 1), 2*c}, 1] == Divide[Gamma[Divide[1,2]]*Gamma[c +Divide[1,2]]*Gamma[Divide[1,2]*(a + b + 1)]*Gamma[c +Divide[1,2]*(1 - a - b)],Gamma[Divide[1,2]*(a + 1)]*Gamma[Divide[1,2]*(b + 1)]*Gamma[c +Divide[1,2]*(1 - a)]*Gamma[c +Divide[1,2]*(1 - b)]]</code> || Successful || Failure || - || Skipped - Because timed out |
| |- | | |- |
| | [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>]] || <code>(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)</code> || <code>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)</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 300]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[q, -1.5]}</code><br><code>Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[q, -1.5]}</code><br></div></div> | | | [https://dlmf.nist.gov/16.4.E7 16.4.E7] || [[Item:Q5201|<math>\genhyperF{3}{2}@@{a,1-a,c}{d,2c-d+1}{1} = \frac{\pi\EulerGamma@{d}\EulerGamma@{2c-d+1}2^{1-2c}}{\EulerGamma@{c+\frac{1}{2}(a-d+1)}\EulerGamma@{c+1-\frac{1}{2}(a+d)}\EulerGamma@{\frac{1}{2}(a+d)}\EulerGamma@{\frac{1}{2}(d-a+1)}}</math>]] || <code>hypergeom([a , 1 - a , c], [d , 2*c - d + 1], 1) = (Pi*GAMMA(d)*GAMMA(2*c - d + 1)*(2)^(1 - 2*c))/(GAMMA(c +(1)/(2)*(a - d + 1))*GAMMA(c + 1 -(1)/(2)*(a + d))*GAMMA((1)/(2)*(a + d))*GAMMA((1)/(2)*(d - a + 1)))</code> || <code>HypergeometricPFQ[{a , 1 - a , c}, {d , 2*c - d + 1}, 1] == Divide[Pi*Gamma[d]*Gamma[2*c - d + 1]*(2)^(1 - 2*c),Gamma[c +Divide[1,2]*(a - d + 1)]*Gamma[c + 1 -Divide[1,2]*(a + d)]*Gamma[Divide[1,2]*(a + d)]*Gamma[Divide[1,2]*(d - a + 1)]]</code> || Successful || Successful || - || Successful [Tested: 40] |
| |- | | |- |
| | [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>]] || <code> 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)</code> || <code> 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)</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 14 / 300]<div class="mw-collapsible-content"><code>{ Indeterminate <- {Rule[a, -1.5], Rule[ k, 2], Rule[ n, 1], Rule[ q, -1 .5]}</code><br><code> Indeterminate <- {Rule[a, -1.5], Rule[ k, 3], Rule[ n, 1], Rule[ q, -1.5]}</code><br></div></div> | | | [https://dlmf.nist.gov/ 16. 4. E8 16. 4. E8] || [[Item: Q5202|<math>\ genhyperF{ 3}{ 2} @@{ -n ,a,1-a}{d,1-d- 2n}{1} = \frac{\ Pochhammersym{ \frac{1}{ 2}(a+d)}{n} \Pochhammersym{\ frac{ 1}{ 2}(d-a +1)}{ n}}{\ Pochhammersym{\frac{ 1}{ 2}d}{ n} \Pochhammersym{\ frac{ 1}{2} (d+1)}{n}}</math>]] || <code> hypergeom( [- n , a , 1 - a], [d , 1 - d - 2*n ], 1) = ( pochhammer((1)/(2)*(a + d), n) *pochhammer((1)/( 2) *( d - a + 1), n)) /(pochhammer(( 1)/( 2)*d, n) *pochhammer((1) /( 2)*( d + 1), n))</code> || <code> HypergeometricPFQ[ {- n , a , 1 - a }, {d , 1 - d - 2*n }, 1] == Divide[ Pochhammer[ Divide[1,2]*(a + d), n] *Pochhammer[Divide[1, 2]*( d - a + 1) , n ], Pochhammer[Divide[1, 2] *d, n]* Pochhammer[Divide[ 1, 2]*( d + 1), n]]</code> || Failure || Failure || Manual Skip! || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 112 / 180]<div class="mw-collapsible-content"><code>{ Complex[-0.5976759376684342, 0.11432617133831768] <- {Rule[a, -1.5], Rule[ d, Power[E, Times[Complex[ 0, Rational[1 , 6]], Pi]]], Rule[ n, 1]}</code><br><code> Complex[-0.4201764035832656, 0.019572796644155455] <- {Rule[a, -1.5], Rule[ d, Power[E, Times[Complex[ 0, Rational[1 , 6]], Pi]]], Rule[ n, 2]}</code><br></div></div> |
| |- | | |- |
| | [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>]] || <code>(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)</code> || <code>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)</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [15 / 300]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 2], Rule[n, 1], Rule[q, -1.5]}</code><br><code>Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[k, 3], Rule[n, 1], Rule[q, -1.5]}</code><br></div></div> | | | [https://dlmf.nist.gov/16.4.E9 16.4.E9] || [[Item:Q5203|<math>\genhyperF{5}{4}@@{a,\frac{1}{2}a+1,b,c,d}{\frac{1}{2}a,a-b+1,a-c+1,a-d+1}{1} = \frac{\EulerGamma@{a-b+1}\EulerGamma@{a-c+1}\EulerGamma@{a-d+1}\EulerGamma@{a-b-c-d+1}}{\EulerGamma@{a+1}\EulerGamma@{a-b-c+1}\EulerGamma@{a-b-d+1}\EulerGamma@{a-c-d+1}}</math>]] || <code>hypergeom([a ,(1)/(2)*a + 1 , b , c , d], [(1)/(2)*a , a - b + 1 , a - c + 1 , a - d + 1], 1) = (GAMMA(a - b + 1)*GAMMA(a - c + 1)*GAMMA(a - d + 1)*GAMMA(a - b - c - d + 1))/(GAMMA(a + 1)*GAMMA(a - b - c + 1)*GAMMA(a - b - d + 1)*GAMMA(a - c - d + 1))</code> || <code>HypergeometricPFQ[{a ,Divide[1,2]*a + 1 , b , c , d}, {Divide[1,2]*a , a - b + 1 , a - c + 1 , a - d + 1}, 1] == Divide[Gamma[a - b + 1]*Gamma[a - c + 1]*Gamma[a - d + 1]*Gamma[a - b - c - d + 1],Gamma[a + 1]*Gamma[a - b - c + 1]*Gamma[a - b - d + 1]*Gamma[a - c - d + 1]]</code> || Failure || Failure || Successful [Tested: 300] || Successful [Tested: 300] |
| |- | | |- |
| | [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>]] || <code> 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)</code> || <code> 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)</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 14 / 300]<div class="mw-collapsible-content"><code> {Indeterminate <- { Rule[a, - 1.5], Rule[k, 1 ], Rule[n, 2 ], Rule[q, -1.5]}</code><br><code> Indeterminate <- { Rule[a, - 1.5], Rule[k, 1 ], Rule[n, 3 ], Rule[q, -1 .5]}</code><br></div></div> | | | [https://dlmf.nist.gov/ 16. 4. E10 16. 4. E10] || [[Item: Q5204|<math>\ genhyperF{7}{6}@@{ a,\frac{1}{ 2}a+1,b,c,d,f,-n} {\frac{1}{ 2}a,a-b+1,a-c+1,a-d+1,a-f+1,a+n+1}{ 1} = \frac{\ Pochhammersym{a +1}{ n}\Pochhammersym{a-b-c+1}{ n}\ Pochhammersym{a -b-d+1}{ n}\Pochhammersym{a-c-d+1}{n}}{\ Pochhammersym{ a-b+1}{n}\Pochhammersym{ a-c+1} {n} \Pochhammersym{ a-d+1}{n} \Pochhammersym{a-b-c-d+1}{ n}}</math>]] || <code> hypergeom( [a ,( 1) /( 2)*a + 1 , b , c , d , f , - n ], [(1) /(2)*a , a - b + 1 , a - c + 1 , a - d + 1 , a - f + 1 , a + n + 1], 1) = ( pochhammer(a + 1, n)*pochhammer(a - b - c + 1, n)* pochhammer(a - b - d + 1, n)*pochhammer(a - c - d + 1, n))/( pochhammer( a - b + 1, n) *pochhammer( a - c + 1 , n) *pochhammer(a - d + 1, n)* pochhammer( a - b - c - d + 1, n ))</code> || <code> HypergeometricPFQ[ {a ,Divide[1,2]* a + 1 , b , c , d , f , - n }, {Divide[1,2]*a , a - b + 1 , a - c + 1 , a - d + 1 , a - f + 1 , a + n + 1}, 1] == Divide[ Pochhammer[a + 1, n]*Pochhammer[a - b - c + 1, n]* Pochhammer[a - b - d + 1, n]*Pochhammer[a - c - d + 1, n], Pochhammer[ a - b + 1 , n]*Pochhammer[a - c + 1, n]*Pochhammer[a - d + 1, n]* Pochhammer[a - b - c - d + 1, n ]]</code> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 299 / 300]<div class="mw-collapsible-content"><code> 299/300]: [[.2096832772+.6841105627e-1*I <- {a = -3/2, b = - 3/2, c = -3/2, d = 1 /2*3^(1/2)+1/2*I, f = 1/2*3^(1/2)+1/2 *I, n = 3}</code><br><code> .1072644549-.5307589441*I <- {a = -3/2, b = - 3/2, c = -3/2, d = 1 /2*3 ^(1/2)+1/2*I, f = -1 /2+1/2*I*3^(1/2), n = 3}</code><br></div></div> || Skipped - Because timed out |
| |- | | |- |
| | [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>]] || <code>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))</code> || <code>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])</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [27 / 300]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[a, -1.5], Rule[k, 1], Rule[n, 1], Rule[q, -1.5]}</code><br><code>Indeterminate <- {Rule[a, -1.5], Rule[k, 1], Rule[n, 2], Rule[q, -1.5]}</code><br></div></div> | | | [https://dlmf.nist.gov/16.4.E11 16.4.E11] || [[Item:Q5205|<math>\genhyperF{3}{2}@@{a,b,c}{d,e}{1} = \frac{\EulerGamma@{e}\EulerGamma@{d+e-a-b-c}}{\EulerGamma@{e-a}\EulerGamma@{d+e-b-c}}\genhyperF{3}{2}@@{a,d-b,d-c}{d,d+e-b-c}{1}</math>]] || <code>hypergeom([a , b , c], [d , e], 1) = (GAMMA(e)*GAMMA(d + e - a - b - c))/(GAMMA(e - a)*GAMMA(d + e - b - c))*hypergeom([a , d - b , d - c], [d , d + e - b - c], 1)</code> || <code>HypergeometricPFQ[{a , b , c}, {d , e}, 1] == Divide[Gamma[e]*Gamma[d + e - a - b - c],Gamma[e - a]*Gamma[d + e - b - c]]*HypergeometricPFQ[{a , d - b , d - c}, {d , d + e - b - c}, 1]</code> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out |
| |- | | |- |
| | [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>]] || <code>QPochhammer(a*(q)^(n), q, k) = (QPochhammer(a, q, k)*QPochhammer(a*(q)^(k), q, n))/(QPochhammer(a, q, n))</code> || <code>QPochhammer[a*(q)^(n), q, k] == Divide[QPochhammer[a, q, k]*QPochhammer[a*(q)^(k), q, n],QPochhammer[a, q, n]]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 300]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[a, -0.5], Rule[k, 1], Rule[n, 2], Rule[q, -2]}</code><br><code>Indeterminate <- {Rule[a, -0.5], Rule[k, 1], Rule[n, 3], Rule[q, -2]}</code><br></div></div> | | | [https://dlmf.nist.gov/16.4.E12 16.4.E12] || [[Item:Q5206|<math>(a-d)(b-d)(c-d)\left(\genhyperF{3}{2}@@{a,b,c}{d+1,e}{1}-\genhyperF{3}{2}@@{a,b,c}{d,e}{1}\right)+abc\genhyperF{3}{2}@@{a,b,c}{d,e}{1} = d(d-1)(a+b+c-d-e+1)\left(\genhyperF{3}{2}@@{a,b,c}{d,e}{1}-\genhyperF{3}{2}@@{a,b,c}{d-1,e}{1}\right)</math>]] || <code>(a - d)*(b - d)*(c - d)*(hypergeom([a , b , c], [d + 1 , e], 1)- hypergeom([a , b , c], [d , e], 1))+ a*b*c*hypergeom([a , b , c], [d , e], 1) = d*(d - 1)*(a + b + c - d - e + 1)*(hypergeom([a , b , c], [d , e], 1)- hypergeom([a , b , c], [d - 1 , e], 1))</code> || <code>(a - d)*(b - d)*(c - d)*(HypergeometricPFQ[{a , b , c}, {d + 1 , e}, 1]- HypergeometricPFQ[{a , b , c}, {d , e}, 1])+ a*b*c*HypergeometricPFQ[{a , b , c}, {d , e}, 1] == d*(d - 1)*(a + b + c - d - e + 1)*(HypergeometricPFQ[{a , b , c}, {d , e}, 1]- HypergeometricPFQ[{a , b , c}, {d - 1 , e}, 1])</code> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out |
| |- | | |- |
| | [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>]] || <code>QPochhammer(a*(q)^(k), q, n - k) = (QPochhammer(a, q, n))/(QPochhammer(a, q, k))</code> || <code>QPochhammer[a*(q)^(k), q, n - k] == Divide[QPochhammer[a, q, n],QPochhammer[a, q, k]]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 300]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[a, -0.5], Rule[k, 2], Rule[n, 1], Rule[q, -2]}</code><br><code>Indeterminate <- {Rule[a, -0.5], Rule[k, 2], Rule[n, 2], Rule[q, -2]}</code><br></div></div> | | | [https://dlmf.nist.gov/16.4.E13 16.4.E13] || [[Item:Q5207|<math>\genhyperF{3}{2}@@{a,b,c}{d,e}{1} = \dfrac{c(e-a)}{de}\genhyperF{3}{2}@@{a,b+1,c+1}{d+1,e+1}{1}+\dfrac{d-c}{d}\genhyperF{3}{2}@@{a,b+1,c}{d+1,e}{1}</math>]] || <code>hypergeom([a , b , c], [d , e], 1) = (c*(e - a))/(d*e)*hypergeom([a , b + 1 , c + 1], [d + 1 , e + 1], 1)+(d - c)/(d)*hypergeom([a , b + 1 , c], [d + 1 , e], 1)</code> || <code>HypergeometricPFQ[{a , b , c}, {d , e}, 1] == Divide[c*(e - a),d*e]*HypergeometricPFQ[{a , b + 1 , c + 1}, {d + 1 , e + 1}, 1]+Divide[d - c,d]*HypergeometricPFQ[{a , b + 1 , c}, {d + 1 , e}, 1]</code> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out |
| |- | | |- |
| | [https://dlmf.nist.gov/17.2.E19 17.2.E19] || [[Item:Q5309|<math>\qPochhammer{a}{q}{2n} = \qmultiPochhammersym{a,aq}{q^{2}}{n}</math>]] || <code>Error</code> || <code>QPochhammer[a, q, 2*n] == Product[QPochhammer[Part[{a , a*q},i],(q)^(2),n],{i,1,Length[{a , a*q}]}]</code> || Error || Failure || - || Successful [Tested: 180] | | | [https://dlmf.nist.gov/16.4.E14 16.4.E14] || [[Item:Q5208|<math>\genhyperF{4}{3}@@{-n,a,b,c}{d,e,f}{1} = \frac{\Pochhammersym{e-a}{n}\Pochhammersym{f-a}{n}}{\Pochhammersym{e}{n}\Pochhammersym{f}{n}}\genhyperF{4}{3}@@{-n,a,d-b,d-c}{d,a-e-n+1,a-f-n+1}{1}</math>]] || <code>hypergeom([- n , a , b , c], [d , e , f], 1) = (pochhammer(e - a, n)*pochhammer(f - a, n))/(pochhammer(e, n)*pochhammer(f, n))*hypergeom([- n , a , d - b , d - c], [d , a - e - n + 1 , a - f - n + 1], 1)</code> || <code>HypergeometricPFQ[{- n , a , b , c}, {d , e , f}, 1] == Divide[Pochhammer[e - a, n]*Pochhammer[f - a, n],Pochhammer[e, n]*Pochhammer[f, n]]*HypergeometricPFQ[{- n , a , d - b , d - c}, {d , a - e - n + 1 , a - f - n + 1}, 1]</code> || Failure || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[-7.272114317029979, 8.095671475544961] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1]}</code><br><code>Complex[-18.740982240718687, 40.16393590217987] <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2]}</code><br></div></div> |
| |- | | |- |
| | [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>]] || <code>QPochhammer((a)^(2), (q)^(2), n) = QPochhammer(a, q, n)*QPochhammer(- a, q, n)</code> || <code>QPochhammer[(a)^(2), (q)^(2), n] == QPochhammer[a, q, n]*QPochhammer[- a, q, n]</code> || Successful || Successful || - || Successful [Tested: 180] | | | [https://dlmf.nist.gov/16.4.E15 16.4.E15] || [[Item:Q5209|<math>\genhyperF{7}{6}@@{a,\frac{1}{2}a+1,b,c,d,e,f}{\frac{1}{2}a,a-b+1,a-c+1,a-d+1,a-e+1,a-f+1}{1} = \frac{\EulerGamma@{a-d+1}\EulerGamma@{a-e+1}\EulerGamma@{a-f+1}\EulerGamma@{a-d-e-f+1}}{\EulerGamma@{a+1}\EulerGamma@{a-d-e+1}\EulerGamma@{a-d-f+1}\EulerGamma@{a-e-f+1}}\genhyperF{4}{3}@@{a-b-c+1,d,e,f}{a-b+1,a-c+1,d+e+f-a}{1}</math>]] || <code>hypergeom([a ,(1)/(2)*a + 1 , b , c , d , e , f], [(1)/(2)*a , a - b + 1 , a - c + 1 , a - d + 1 , a - e + 1 , a - f + 1], 1) = (GAMMA(a - d + 1)*GAMMA(a - e + 1)*GAMMA(a - f + 1)*GAMMA(a - d - e - f + 1))/(GAMMA(a + 1)*GAMMA(a - d - e + 1)*GAMMA(a - d - f + 1)*GAMMA(a - e - f + 1))*hypergeom([a - b - c + 1 , d , e , f], [a - b + 1 , a - c + 1 , d + e + f - a], 1)</code> || <code>HypergeometricPFQ[{a ,Divide[1,2]*a + 1 , b , c , d , e , f}, {Divide[1,2]*a , a - b + 1 , a - c + 1 , a - d + 1 , a - e + 1 , a - f + 1}, 1] == Divide[Gamma[a - d + 1]*Gamma[a - e + 1]*Gamma[a - f + 1]*Gamma[a - d - e - f + 1],Gamma[a + 1]*Gamma[a - d - e + 1]*Gamma[a - d - f + 1]*Gamma[a - e - f + 1]]*HypergeometricPFQ[{a - b - c + 1 , d , e , f}, {a - b + 1 , a - c + 1 , d + e + f - a}, 1]</code> || Failure || Aborted || Skipped - Because timed out || Skipped - Because timed out |
| |- | | |- |
| | [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>]] || <code>Error</code> || <code>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]]</code> || Error || Successful || - || Successful [Tested: 180] | | | [https://dlmf.nist.gov/16.6.E1 16.6.E1] || [[Item:Q5216|<math>\genhyperF{3}{2}@@{a,b,c}{a-b+1,a-c+1}{z} = (1-z)^{-a}\genhyperF{3}{2}@@{a-b-c+1,\frac{1}{2}a,\frac{1}{2}(a+1)}{a-b+1,a-c+1}{\frac{-4z}{(1-z)^{2}}}</math>]] || <code>hypergeom([a , b , c], [a - b + 1 , a - c + 1], z) = (1 - z)^(- a)* hypergeom([a - b - c + 1 ,(1)/(2)*a ,(1)/(2)*(a + 1)], [a - b + 1 , a - c + 1], (- 4*z)/((1 - z)^(2)))</code> || <code>HypergeometricPFQ[{a , b , c}, {a - b + 1 , a - c + 1}, z] == (1 - z)^(- a)* HypergeometricPFQ[{a - b - c + 1 ,Divide[1,2]*a ,Divide[1,2]*(a + 1)}, {a - b + 1 , a - c + 1}, Divide[- 4*z,(1 - z)^(2)]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [258 / 300]<div class="mw-collapsible-content"><code>258/300]: [[-2.076719790+.860205503*I <- {a = -3/2, b = -3/2, c = -3/2, z = 1/2*3^(1/2)+1/2*I}</code><br><code>-1.428233246+.1e-8*I <- {a = -3/2, b = -3/2, c = -3/2, z = 1/2-1/2*I*3^(1/2)}</code><br></div></div> || Skipped - Because timed out |
| |- | | |- |
| | [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>]] || <code>(QPochhammer(a*(q)^(2), (q)^(2), n))/(QPochhammer(a, (q)^(2), n)) = (1 - a*(q)^(2*n))/(1 - a)</code> || <code>Divide[QPochhammer[a*(q)^(2), (q)^(2), n],QPochhammer[a, (q)^(2), n]] == Divide[1 - a*(q)^(2*n),1 - a]</code> || Successful || Failure || - || Successful [Tested: 180] | | | [https://dlmf.nist.gov/16.6.E2 16.6.E2] || [[Item:Q5217|<math>\genhyperF{3}{2}@@{a,2b-a-1,2-2b+a}{b,a-b+\frac{3}{2}}{\frac{z}{4}} = (1-z)^{-a}\genhyperF{3}{2}@@{\frac{1}{3}a,\frac{1}{3}a+\frac{1}{3},\frac{1}{3}a+\frac{2}{3}}{b,a-b+\frac{3}{2}}{\frac{-27z}{4(1-z)^{3}}}</math>]] || <code>hypergeom([a , 2*b - a - 1 , 2 - 2*b + a], [b , a - b +(3)/(2)], (z)/(4)) = (1 - z)^(- a)* hypergeom([(1)/(3)*a ,(1)/(3)*a +(1)/(3),(1)/(3)*a +(2)/(3)], [b , a - b +(3)/(2)], (- 27*z)/(4*(1 - z)^(3)))</code> || <code>HypergeometricPFQ[{a , 2*b - a - 1 , 2 - 2*b + a}, {b , a - b +Divide[3,2]}, Divide[z,4]] == (1 - z)^(- a)* HypergeometricPFQ[{Divide[1,3]*a ,Divide[1,3]*a +Divide[1,3],Divide[1,3]*a +Divide[2,3]}, {b , a - b +Divide[3,2]}, Divide[- 27*z,4*(1 - z)^(3)]]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [216 / 252]<div class="mw-collapsible-content"><code>216/252]: [[.1888061791+.200959324e-1*I <- {a = -3/2, b = -3/2, z = 1/2*3^(1/2)+1/2*I}</code><br><code>-.140210603-.95166922e-1*I <- {a = -3/2, b = -3/2, z = -1/2+1/2*I*3^(1/2)}</code><br></div></div> || Skipped - Because timed out |
| |- | | |- |
| | [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>]] || <code>(QPochhammer(a*(q)^(k), (q)^(k), n))/(QPochhammer(a, (q)^(k), n)) = (1 - a*(q)^(k*n))/(1 - a)</code> || <code>Divide[QPochhammer[a*(q)^(k), (q)^(k), n],QPochhammer[a, (q)^(k), n]] == Divide[1 - a*(q)^(k*n),1 - a]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 300]<div class="mw-collapsible-content"><code>{Indeterminate <- {Rule[a, -0.5], Rule[k, 1], Rule[n, 2], Rule[q, -2]}</code><br><code>Indeterminate <- {Rule[a, -0.5], Rule[k, 1], Rule[n, 3], Rule[q, -2]}</code><br></div></div> | | | [https://dlmf.nist.gov/16.8.E4 16.8.E4] || [[Item:Q5222|<math>z^{q}D^{q+1}w+\sum_{j=1}^{q}z^{j-1}(\alpha_{j}z+\beta_{j})D^{j}w+\alpha_{0}w = 0</math>]] || <code>(z)^(q)* (D)^(q + 1)* w + sum((z)^(j - 1)*(alpha[j]*z + beta[j])* (D)^(j)* w , j = 1..q)+ alpha[0]*w = 0</code> || <code>(z)^(q)* (D)^(q + 1)* w + Sum[(z)^(j - 1)*(Subscript[\[Alpha], j]*z + Subscript[\[Beta], j])* (D)^(j)* w , {j, 1, q}, GenerateConditions->None]+ Subscript[\[Alpha], 0]*w == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || - |
| |- | | |- |
| | [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>]] || <code>limit(QPochhammer(a/ tau, q, n)*(tau)^(n), tau = 0) = limit(QPochhammer(a*sigma, q, n)*(sigma)^(- n), sigma = infinity)</code> || <code>Limit[QPochhammer[a/ \[Tau], q, n]*\[Tau]^(n), \[Tau] -> 0, GenerateConditions->None] == Limit[QPochhammer[a*\[Sigma], q, n]*\[Sigma]^(- n), \[Sigma] -> Infinity, GenerateConditions->None]</code> || Failure || Failure || Error || Successful [Tested: 180] | | | [https://dlmf.nist.gov/16.8.E5 16.8.E5] || [[Item:Q5223|<math>z^{q}(1-z)D^{q+1}w+\sum_{j=1}^{q}z^{j-1}(\alpha_{j}z+\beta_{j})D^{j}w+\alpha_{0}w = 0</math>]] || <code>(z)^(q)*(1 - z)* (D)^(q + 1)* w + sum((z)^(j - 1)*(alpha[j]*z + beta[j])* (D)^(j)* w , j = 1..q)+ alpha[0]*w = 0</code> || <code>(z)^(q)*(1 - z)* (D)^(q + 1)* w + Sum[(z)^(j - 1)*(Subscript[\[Alpha], j]*z + Subscript[\[Beta], j])* (D)^(j)* w , {j, 1, q}, GenerateConditions->None]+ Subscript[\[Alpha], 0]*w == 0</code> || Skipped - no semantic math || Skipped - no semantic math || - || - |
| |- | | |- |
| | [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>]] || <code>limit(QPochhammer(a*sigma, q, n)*(sigma)^(- n), sigma = infinity) = (- a)^(n)* (q)^(binomial(n,2))</code> || <code>Limit[QPochhammer[a*\[Sigma], q, n]*\[Sigma]^(- n), \[Sigma] -> Infinity, GenerateConditions->None] == (- a)^(n)* (q)^(Binomial[n,2])</code> || Failure || Failure || Error || Successful [Tested: 180] | | | [https://dlmf.nist.gov/16.11#Ex3 16.11#Ex3] || [[Item:Q5237|<math>c_{0} = 1</math>]] || <code>c[0] = 1</code> || <code>Subscript[c, 0] == 1</code> || Skipped - no semantic math || Skipped - no semantic math || - || - |
| |- | | |- |
| | [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>]] || <code>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)</code> || <code>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]</code> || Failure || Failure || Error || Successful [Tested: 300] | | | [https://dlmf.nist.gov/16.11#Ex4 16.11#Ex4] || [[Item:Q5238|<math>c_{k} = -\frac{1}{k\kappa^{\kappa}}\sum_{m=0}^{k-1}c_{m}e_{k,m}</math>]] || <code>c[k] = -(1)/(k*(kappa)^(kappa))*sum(c[m]*e[k , m], m = 0..k - 1)</code> || <code>Subscript[c, k] == -Divide[1,k*\[Kappa]^\[Kappa]]*Sum[Subscript[c, m]*Subscript[e, k , m], {m, 0, k - 1}, GenerateConditions->None]</code> || Skipped - no semantic math || Skipped - no semantic math || - || - |
| |- | | |- |
| | [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>]] || <code>limit((QPochhammer(a*sigma, q, n))/(QPochhammer(b*sigma, q, n)), sigma = infinity) = ((a)/(b))^(n)</code> || <code>Limit[Divide[QPochhammer[a*\[Sigma], q, n],QPochhammer[b*\[Sigma], q, n]], \[Sigma] -> Infinity, GenerateConditions->None] == (Divide[a,b])^(n)</code> || Failure || Failure || Error || Successful [Tested: 300] | | | [https://dlmf.nist.gov/16.12.E1 16.12.E1] || [[Item:Q5246|<math>\genhyperF{0}{1}@{-}{a}{z}\genhyperF{0}{1}@{-}{b}{z} = \genhyperF{2}{3}@@{\frac{1}{2}(a+b),\frac{1}{2}(a+b-1)}{a,b,a+b-1}{4z}</math>]] || <code>hypergeom([-], [a], z)*hypergeom([-], [b], z) = hypergeom([(1)/(2)*(a + b),(1)/(2)*(a + b - 1)], [a , b , a + b - 1], 4*z)</code> || <code>HypergeometricPFQ[{-}, {a}, z]*HypergeometricPFQ[{-}, {b}, z] == HypergeometricPFQ[{Divide[1,2]*(a + b),Divide[1,2]*(a + b - 1)}, {a , b , a + b - 1}, 4*z]</code> || Error || Failure || - || Error |
| |- | | |- |
| | [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>]] || <code>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))</code> || <code>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])</code> || Error || Failure || - || Successful [Tested: 300] | | | [https://dlmf.nist.gov/16.12.E2 16.12.E2] || [[Item:Q5247|<math>\left(\genhyperF{2}{1}@@{a,b}{a+b+\frac{1}{2}}{z}\right)^{2} = \genhyperF{3}{2}@@{2a,2b,a+b}{a+b+\frac{1}{2},2a+2b}{z}</math>]] || <code>(hypergeom([a , b], [a + b +(1)/(2)], z))^(2) = hypergeom([2*a , 2*b , a + b], [a + b +(1)/(2), 2*a + 2*b], z)</code> || <code>(HypergeometricPFQ[{a , b}, {a + b +Divide[1,2]}, z])^(2) == HypergeometricPFQ[{2*a , 2*b , a + b}, {a + b +Divide[1,2], 2*a + 2*b}, z]</code> || Failure || Failure || Manual Skip! || <div class="toccolours mw-collapsible mw-collapsed">Failed [108 / 252]<div class="mw-collapsible-content"><code>{Complex[4.205771365940054, 0.2846096908265261] <- {Rule[a, -1.5], Rule[b, 1.5], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-23.50000000000001, -28.578838324886455] <- {Rule[a, -1.5], Rule[b, 1.5], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div> |
| |- | | |- |
| | [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>]] || <code> QBinomial( n, m, q) = ( QPochhammer( q, q, n))/( QPochhammer( q, q, m)* QPochhammer( q, q, n - m))</code> || <code> QBinomial[ n, m, q] == Divide[ QPochhammer[ q, q, n], QPochhammer[ q, q, m]* QPochhammer[ q, q, n - m]]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 1 / 90]<div class="mw-collapsible-content"><code> {Complex[- 0.058394160583941646, 0. 1605839416058394] <- { Rule[m, 3 ], Rule[n, 1 ], Rule[q, Power[E, Times[Complex[0, Rational[2 , 3]], Pi]]]}</code><br></div></div> | | | [https://dlmf.nist.gov/ 16. 12. E3 16. 12. E3] || [[Item: Q5248|<math>\ left(\genhyperF{2}{1}@@{ a,b}{ c}{ z}\right)^{2} = \sum_{k=0}^{\infty}\frac{\ Pochhammersym{ 2a}{ k} \Pochhammersym{ 2b} {k} \Pochhammersym{ c-\ frac{ 1}{ 2}}{ k} }{\ Pochhammersym{ c}{ k} \Pochhammersym{ 2c- 1}{k}k!}\genhyperF{4} {3} @@{-\ frac{1}{2}k,\ frac{1}{2}(1-k),a+b-c+\frac{1}{2},\frac{1}{2}}{a+\frac{1}{2},b+\frac{1}{2},\frac{3}{2}-k-c}{1}z^{k}</math>]] || <code>( hypergeom([a , b], [c], z))^(2) = sum(( pochhammer(2*a, k)*pochhammer(2*b, k)*pochhammer(c -(1)/(2), k))/( pochhammer( c, k)*pochhammer(2*c - 1, k)* factorial(k))*hypergeom([-(1)/( 2)*k , (1)/(2)*(1 - k), a + b - c +(1)/(2) ,(1)/(2)], [a +(1)/(2), b +(1)/(2),(3)/(2)- k - c], 1)*(z)^(k), k = 0..infinity)</code> || <code> (HypergeometricPFQ[ {a , b}, {c}, z] )^(2) == Sum[Divide[ Pochhammer[ 2*a, k]*Pochhammer[2*b, k] *Pochhammer[c -Divide[1,2], k],Pochhammer[c, k]*Pochhammer[2*c - 1, k]*(k)!]*HypergeometricPFQ[ {-Divide[1,2]*k , Divide[1, 2]* (1 - k), a + b - c +Divide[ 1,2],Divide[1,2]}, {a +Divide[1,2], b +Divide[1,2], Divide[3, 2]- k - c}, 1] *(z)^(k), {k, 0, Infinity}, GenerateConditions->None]</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 159 / 216]<div class="mw-collapsible-content"><code> 159/216]: [[-. 1250000000 <- { a = -3/2, b = -3 /2, c = -3/2, z = 1 /2}</code><br><code>5.872053804 <- {a = -3/2, b = -3/2, c = -1/2, z = 1/2}</code><br></div></div> || Skipped - Because timed out |
| |- | | |- |
| | [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>]] || <code> (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))</code> || <code> 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]]</code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 3 / 90]<div class="mw-collapsible-content"><code>{Complex[0. 11678832116788332, -0. 3211678832116788] <- {Rule[ m, 3], Rule[ n, 1], Rule[ q, Power[E, Times[Complex[0, Rational[ 2, 3]], Pi]]]}</code><br><code>Complex[1.0, 0.0] <- {Rule[ m, 3], Rule[ n, 2], Rule[ q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div> | | | [https://dlmf.nist.gov/ 16. 16. E5 16. 16. E5] || [[Item: Q5271|<math>\ AppellF{ 3} @{ \alpha}{ \gamma-\alpha}{\ beta}{\ gamma- \beta}{\ gamma}{ x}{ y} = ( 1- y)^{ \alpha+\beta-\ gamma} \genhyperF{2} {1} @@{\ alpha,\beta}{ \gamma}{ x+y-xy}</math>]] || <code> Error</code> || <code> AppellF[ 3, , \[Alpha], \[ Gamma] - \[ Alpha], \[Beta], \[Gamma]- \[Beta]] *\[Gamma]*x*y == ( 1 - y)^( \[Alpha]+ \[Beta]- \[Gamma])* HypergeometricPFQ[{\[ Alpha], \[Beta] }, {\[ Gamma]}, x + y - x*y]</code> || Missing Macro Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 300 / 300]<div class="mw-collapsible-content"><code>{ Plus[Complex[0. 33907796278424684, 2.1694931088262193], Times[Complex[-1.948557158514987, -1.1249999999999998], AppellF[3.0, Null, 1.5, Complex[-0. 6339745962155613, 0.49999999999999994], 1.5, Complex[-0.6339745962155613, 0.49999999999999994]]]] <- {Rule[ x, 1.5], Rule[y, -1.5], Rule[α, 1.5], Rule[ β, 1 .5], Rule[ γ, Power[E, Times[Complex[0, Rational[ 1, 6]], Pi]]]}</code><br><code> Plus[Complex[3.1592684418872854, 2.774129956365469], Times[Complex[1 .1249999999999996, -1.948557158514987], AppellF[3.0 , Null, 1.5, Complex[-1.9999999999999998, 0. 8660254037844387], 1.5, Complex[-1.9999999999999998, 0 .8660254037844387]]]] <- {Rule[ x, 1.5], Rule[y, -1.5], Rule[α, 1.5], Rule[ β, 1.5], Rule[ γ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div> |
| |- | | |- |
| | [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>]] || <code>limit(QBinomial(n, m, q), q = 1) = binomial(n,m)</code> || <code>Limit[QBinomial[n,m,q], q -> 1, GenerateConditions->None] == Binomial[n,m]</code> || Failure || Error || Error || Skipped - Because timed out | | | [https://dlmf.nist.gov/16.16.E6 16.16.E6] || [[Item:Q5272|<math>\AppellF{4}@{\alpha}{\beta}{\gamma}{\alpha+\beta-\gamma+1}{x(1-y)}{y(1-x)} = \genhyperF{2}{1}@@{\alpha,\beta}{\gamma}{x}\genhyperF{2}{1}@@{\alpha,\beta}{\alpha+\beta-\gamma+1}{y}</math>]] || <code>Error</code> || <code>AppellF[4, , \[Alpha], \[Beta], \[Gamma], \[Alpha]+ \[Beta]- \[Gamma]+ 1]*x*(1 - y)*y*(1 - x) == HypergeometricPFQ[{\[Alpha], \[Beta]}, {\[Gamma]}, x]*HypergeometricPFQ[{\[Alpha], \[Beta]}, {\[Alpha]+ \[Beta]- \[Gamma]+ 1}, y]</code> || Missing Macro Error || Failure || - || Skip - No test values generated |
| |- | | |- |
| | [https://dlmf.nist.gov/17.2.E28 17.2.E28] || [[Item:Q5318|<math>\binom{n}{m} = \frac{n!}{m!(n-m)!}</math>]] || <code>binomial(n,m) = (factorial(n))/(factorial(m)*factorial(n - m))</code> || <code>Binomial[n,m] == Divide[(n)!,(m)!*(n - m)!]</code> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 9] | | | [https://dlmf.nist.gov/ 16. 23. E1 16. 23. E1] || [[Item: Q5289|<math>\ genhyperF{ 3}{2}@@{-n,n +\alpha+2,\frac{1}{ 2} (\alpha+1)}{\alpha+1,\frac{ 1}{ 2}( \alpha+3)} {x} > 0</math>]] || <code> hypergeom( [- n , n + alpha + 2 ,( 1)/( 2)*( alpha + 1) ], [alpha + 1 ,(1)/(2)*(alpha + 3)], x) > 0</code> || <code> HypergeometricPFQ[ {- n , n + \[Alpha] + 2 ,Divide[ 1,2]*( \[Alpha]+ 1) }, {\[Alpha]+ 1 ,Divide[1,2]*( \[Alpha]+ 3) }, x] > 0</code> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 12 / 27] <div class="mw-collapsible- content"><code>12/27]: [[ 0. < -. 5000000000 <- {alpha = 3/2 , x = 3/2 , n = 1}</code>< br> <code>0. < -1.482142857 <- { alpha = 3/ 2, x = 3/ 2, n = 3}</code>< br></div></ div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 12 / 27]<div class="mw-collapsible-content"><code>{ False <- {Rule[ n, 1], Rule[ x, 1 .5], Rule[ α, 1.5]}</code><br><code> False <- {Rule[ n, 3], Rule[ x, 1.5], Rule[ α, 1.5]}</code><br></div></div> |
| |-
| |
| | [ 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>]] || <code>QBinomial(m + n, m, q) = (QPochhammer((q)^(n + 1), q, m))/ (QPochhammer(q, q, m))</code> || < code> QBinomial[m + n,m,q] == Divide[QPochhammer[(q)^(n + 1), q, m],QPochhammer[q, q, m]]</ code> || Successful || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [ 3 / 90]<div class="mw-collapsible-content"><code>{ Complex[0.9416058394160581, 0.1605839416058394] <- {Rule[ m, 3], Rule[ n, 1], Rule[ q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br><code> Complex[ 1.0, 0.0] <- {Rule[m, 3], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div> | |
| |-
| |
| | [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>]] || <code>QBinomial(- n, m, q) = QBinomial(m + n - 1, m, q)*(- 1)^(m)* (q)^(- m*n -binomial(m,2))</code> || <code>QBinomial[- n,m,q] == QBinomial[m + n - 1,m,q]*(- 1)^(m)* (q)^(- m*n -Binomial[m,2])</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [84 / 90]<div class="mw-collapsible-content"><code>{Complex[0.7320508075688774, 0.0] <- {Rule[m, 1], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-2.3660254037844384, -1.3660254037844386] <- {Rule[m, 1], Rule[n, 3], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
| |
| |-
| |
| | [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>]] || <code>QBinomial(n, m, q) = QBinomial(n - 1, m - 1, q)+ (q)^(m)* QBinomial(n - 1, m, q)</code> || <code>QBinomial[n,m,q] == QBinomial[n - 1,m - 1,q]+ (q)^(m)* QBinomial[n - 1,m,q]</code> || Successful || Failure || - || Successful [Tested: 90]
| |
| |-
| |
| | [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>]] || <code>QBinomial(n, m, q) = QBinomial(n - 1, m, q)+ (q)^(n - m)* QBinomial(n - 1, m - 1, q)</code> || <code>QBinomial[n,m,q] == QBinomial[n - 1,m,q]+ (q)^(n - m)* QBinomial[n - 1,m - 1,q]</code> || Successful || Failure || - || Successful [Tested: 90]
| |
| |-
| |
| | [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>]] || <code>limit(QBinomial(n, m, q), n = infinity) = (1)/(QPochhammer(q, q, m))</code> || <code>Limit[QBinomial[n,m,q], n -> Infinity, GenerateConditions->None] == Divide[1,QPochhammer[q, q, m]]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [24 / 30]<div class="mw-collapsible-content"><code>{Plus[Complex[-0.5, -1.866025403784439], Times[Complex[-0.5, -1.866025403784439], Plus[-1.0, Power[2.718281828459045, Times[Complex[0.0, 2.0], Interval[{-2.2250738585072014*^-308, 3.1415926535897936}]]]]]] <- {Rule[m, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[1.3660254037844395, -1.3660254037844388], Times[Complex[0.5000000000000009, -1.866025403784439], Plus[-1.0, Power[2.718281828459045, Times[Complex[0.0, 2.0], Interval[{-2.2250738585072014*^-308, 3.1415926535897936}]]]], Plus[Complex[0.8660254037844387, 0.49999999999999994], Power[2.718281828459045, Times[Complex[0.0, 2.0], Interval[{-2.2250738585072014*^-308, 3.1415926535897936}]]]]]] <- {Rule[m, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
| |
| |-
| |
| | [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>]] || <code>limit(QBinomial(r*n + u, sn(+)*t, q), n = infinity) = (1)/(QPochhammer(q, q, infinity))</code> || <code>Limit[QBinomial[r*n + u,sn(+)*t,q], n -> Infinity, GenerateConditions->None] == Divide[1,QPochhammer[q, q, Infinity]]</code> || Error || Failure || Skip - symbolical successful subtest || Error
| |
| |-
| |
| | [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>]] || <code>(1)/(QPochhammer(q, q, infinity)) = product((1)/(1 - (q)^(j)), j = 1..infinity)</code> || <code>Divide[1,QPochhammer[q, q, Infinity]] == Product[Divide[1,1 - (q)^(j)], {j, 1, Infinity}, GenerateConditions->None]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 10]<div class="mw-collapsible-content"><code>{Plus[Times[-1.0, Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], -1]], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]] <- {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Times[-1.0, Power[QPochhammer[Complex[0.5000000000000001, -0.8660254037844386], Complex[0.5000000000000001, -0.8660254037844386]], -1]], Power[QPochhammer[Complex[0.5000000000000001, -0.8660254037844386], Complex[0.5000000000000001, -0.8660254037844386], DirectedInfinity[1]], -1]] <- {Rule[q, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</code><br></div></div>
| |
| |-
| |
| | [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>]] || <code>sum(QBinomial(n, j, q)*(- z)^(j)* (q)^(binomial(j,2)), j = 0..n) = QPochhammer(z, q, n)</code> || <code>Sum[QBinomial[n,j,q]*(- z)^(j)* (q)^(Binomial[j,2]), {j, 0, n}, GenerateConditions->None] == QPochhammer[z, q, n]</code> || 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>]] || <code>sum(binomial(n,j)*(- z)^(j), j = 0..n) = (1 - z)^(n)</code> || <code>Sum[Binomial[n,j]*(- z)^(j), {j, 0, n}, GenerateConditions->None] == (1 - z)^(n)</code> || 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>]] || <code>sum((QPochhammer(a, q, n))/(QPochhammer(q, q, n))*(z)^(n), n = 0..infinity) = (QPochhammer(a*z, q, infinity))/(QPochhammer(z, q, infinity))</code> || <code>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]]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><code>{Plus[Times[QPochhammer[Complex[-1.299038105676658, -0.7499999999999999], Complex[0.8660254037844387, 0.49999999999999994]], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], -1]], Times[-1.0, QPochhammer[Complex[-1.299038105676658, -0.7499999999999999], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]]] <- {Rule[a, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Times[Power[QPochhammer[Complex[-0.4999999999999998, 0.8660254037844387], Complex[0.8660254037844387, 0.49999999999999994]], -1], QPochhammer[Complex[0.7499999999999997, -1.299038105676658], Complex[0.8660254037844387, 0.49999999999999994]]], Times[-1.0, Power[QPochhammer[Complex[-0.4999999999999998, 0.8660254037844387], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[0.7499999999999997, -1.299038105676658], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]] <- {Rule[a, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>sum(QBinomial(n + m, n, q)*(z)^(n), n = 0..infinity) = (1)/(QPochhammer(z, q, m + 1))</code> || <code>Sum[QBinomial[n + m,n,q]*(z)^(n), {n, 0, Infinity}, GenerateConditions->None] == Divide[1,QPochhammer[z, q, m + 1]]</code> || Failure || Error || Error || Skipped - Because timed out
| |
| |-
| |
| | [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>]] || <code>sum(QBinomial(n, j, (q)^(2))*(q)^(j), j = 0..n) = QPochhammer(- q, q, n)</code> || <code>Sum[QBinomial[n,j,(q)^(2)]*(q)^(j), {j, 0, n}, GenerateConditions->None] == QPochhammer[- q, q, n]</code> || Failure || Error || Error || Successful [Tested: 30]
| |
| |-
| |
| | [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>]] || <code>sum((- 1)^(j)* QBinomial(2*n, j, q), j = 0..2*n) = QPochhammer(q, (q)^(2), n)</code> || <code>Sum[(- 1)^(j)* QBinomial[2*n,j,q], {j, 0, 2*n}, GenerateConditions->None] == QPochhammer[q, (q)^(2), n]</code> || 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>]] || <code>sum(((1 - q)^(n)* (x)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = (1)/(QPochhammer((1 - q)* x, q, infinity))</code> || <code>Sum[Divide[(1 - q)^(n)* (x)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == Divide[1,QPochhammer[(1 - q)* x, q, Infinity]]</code> || Failure || Error || Error || Skipped - Because timed out
| |
| |-
| |
| | [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>]] || <code>sum(((1 - q)^(n)* (q)^(binomial(n,2))* (x)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = QPochhammer(-(1 - q)* x, q, infinity)</code> || <code>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]</code> || Failure || Error || Error || Skipped - Because timed out
| |
| |-
| |
| | [https://dlmf.nist.gov/17.4.E11 17.4.E11] || [[Item:Q5360|<math>a_{0}q = a_{1}b_{1}</math>]] || <code>a[0]*q = a[1]*b[1]</code> || <code>Subscript[a, 0]*q == Subscript[a, 1]*Subscript[b, 1]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/17.4.E12 17.4.E12] || [[Item:Q5361|<math>b_{1} = -b_{2}</math>]] || <code>b[1] = - b[2]</code> || <code>Subscript[b, 1] == - Subscript[b, 2]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [https://dlmf.nist.gov/17.4.E13 17.4.E13] || [[Item:Q5362|<math>a_{0}q = a_{1}b_{1}</math>]] || <code>a[0]*q = a[1]*b[1]</code> || <code>Subscript[a, 0]*q == Subscript[a, 1]*Subscript[b, 1]</code> || Skipped - no semantic math || Skipped - no semantic math || - || -
| |
| |-
| |
| | [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>]] || <code>Error</code> || <code>QHypergeometricPFQ[{-},{-},q,z] == Sum[Divide[(- 1)^(n)* (q)^(Binomial[n,2])* (z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || Skip - symbolical successful subtest || Error
| |
| |-
| |
| | [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>]] || <code>sum(((- 1)^(n)* (q)^(binomial(n,2))* (z)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = QPochhammer(z, q, infinity)</code> || <code>Sum[Divide[(- 1)^(n)* (q)^(Binomial[n,2])* (z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == QPochhammer[z, q, Infinity]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [8 / 10]<div class="mw-collapsible-content"><code>{Plus[QPochhammer[0.5, Complex[0.8660254037844387, 0.49999999999999994]], Times[-1.0, QPochhammer[0.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]] <- {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, 0.5]}</code><br><code>Indeterminate <- {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[z, 0.5]}</code><br></div></div>
| |
| |-
| |
| | [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>]] || <code>Error</code> || <code>QHypergeometricPFQ[{a},{-},q,z] == Divide[QPochhammer[a*z, q, Infinity],QPochhammer[z, q, Infinity]]</code> || Error || Failure || - || Error
| |
| |-
| |
| | [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>]] || <code>Error</code> || <code>QHypergeometricPFQ[{(q)^(- n)},{-},q,z] == QPochhammer[z*(q)^(- n), q, n]</code> || Error || Failure || - || Error
| |
| |-
| |
| | [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>]] || <code>Error</code> || <code>QHypergeometricPFQ[{0},{-},q,z] == Sum[Divide[(z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None]</code> || Error || Failure || Skip - symbolical successful subtest || Error
| |
| |-
| |
| | [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>]] || <code>sum(((z)^(n))/(QPochhammer(q, q, n)), n = 0..infinity) = (1)/(QPochhammer(z, q, infinity))</code> || <code>Sum[Divide[(z)^(n),QPochhammer[q, q, n]], {n, 0, Infinity}, GenerateConditions->None] == Divide[1,QPochhammer[z, q, Infinity]]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [8 / 10]<div class="mw-collapsible-content"><code>{Plus[QHypergeometricPFQ[{0.0} <- {}, Complex[0.8660254037844387, 0.49999999999999994], 0.5], Times[-1.0, Power[QPochhammer[0.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, 0.5]}</code><br><code>QHypergeometricPFQ[{0.0} <- {}, Complex[-0.4999999999999998, 0.8660254037844387], 0.5], {Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]], Rule[z, 0.5]}</code><br></div></div>
| |
| |-
| |
| | [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>]] || <code>Error</code> || <code>QHypergeometricPFQ[{a},{c},q,c/ a] == Divide[QPochhammer[c/ a, q, Infinity],QPochhammer[c, q, Infinity]]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [96 / 120]<div class="mw-collapsible-content"><code>{Plus[QHypergeometricPFQ[{-1.5} <- {-0.5}, Complex[0.8660254037844387, 0.49999999999999994], 0.3333333333333333], Times[-1.0, Power[QPochhammer[-0.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[0.3333333333333333, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]], {Rule[a, -1.5], Rule[c, -0.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Indeterminate <- {Rule[a, -1.5], Rule[c, -0.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
| |
| |-
| |
| | [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>]] || <code>Error</code> || <code>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)}]}]]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [262 / 300]<div class="mw-collapsible-content"><code>{Plus[0.0, QHypergeometricPFQ[{-1.5, -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], -0.6666666666666666]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[0.0, QHypergeometricPFQ[{-1.5, -1.5} <- {-1.5}, Complex[-0.4999999999999998, 0.8660254037844387], -0.6666666666666666]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></div></div>
| |
| |-
| |
| | [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>]] || <code>Error</code> || <code>QHypergeometricPFQ[{a , (q)^(- n)},{c},q,Divide[c*(q)^(n),a]] == Divide[QPochhammer[c/ a, q, n],QPochhammer[c, q, n]]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [204 / 300]<div class="mw-collapsible-content"><code>{Plus[0.0, QHypergeometricPFQ[{-1.5, Complex[0.8660254037844387, -0.49999999999999994]} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[a, -1.5], Rule[c, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[0.5000000000000001, -0.8660254037844386]} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.5000000000000001, 0.8660254037844386]]], {Rule[a, -1.5], Rule[c, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></div></div>
| |
| |-
| |
| | [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>]] || <code>Error</code> || <code>QHypergeometricPFQ[{a , (q)^(- n)},{c},q,q] == Divide[(a)^(n)* QPochhammer[c/ a, q, n],QPochhammer[c, q, n]]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [168 / 300]<div class="mw-collapsible-content"><code>{Plus[0.0, QHypergeometricPFQ[{-1.5, Complex[0.8660254037844387, -0.49999999999999994]} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[a, -1.5], Rule[c, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[0.5000000000000001, -0.8660254037844386]} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[a, -1.5], Rule[c, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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]])</code> || 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>]] || <code>Error</code> || <code>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}]}]]</code> || 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>]] || <code>Error</code> || <code>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]</code> || Error || Failure || - || Skip - No test values generated
| |
| |-
| |
| | [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>]] || <code>Error</code> || <code>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]</code> || 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>]] || <code>Error</code> || <code>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]]</code> || Error || Failure || - || Skip - No test values generated
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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>]] || <code>Error</code> || <code>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}]}]]</code> || Error || Failure || - || 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>]] || <code>Error</code> || <code>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]</code> || Error || Failure || - || Skip - No test values generated
| |
| |-
| |
| | [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>]] || <code>Error</code> || <code>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)]</code> || 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>]] || <code>Error</code> || <code>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]</code> || 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>]] || <code>Error</code> || <code>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]</code> || 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>]] || <code>Error</code> || <code>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]</code> || 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>]] || <code>Error</code> || <code>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]</code> || 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>]] || <code>Error</code> || <code>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]</code> || 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>]] || <code>Error</code> || <code>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]</code> || 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>]] || <code>Error</code> || <code>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]</code> || 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>]] || <code>Error</code> || <code>(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]</code> || 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>]] || <code>Error</code> || <code>(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]</code> || 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>]] || <code>Error</code> || <code>(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)]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [264 / 300]<div class="mw-collapsible-content"><code>{Plus[0.0, Times[Complex[0.8660254037844387, 0.49999999999999994], QHypergeometricPFQ[{-1.5, -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Power[QPochhammer[Complex[-1.299038105676658, -0.7499999999999999], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[D, q], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.0, 0.0], Times[Complex[0.5000000000000001, 0.8660254037844386], QHypergeometricPFQ[{-1.5, -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Power[QPochhammer[Complex[-1.299038105676658, -0.7499999999999999], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[D, q], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Times[Complex[9.528684177437189, -1.3259618943233384], QHypergeometricPFQ[{-1.5, -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[D, q], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Times[Complex[5.290063509461103, -21.657849302036027], QHypergeometricPFQ[{-1.5, -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[D, q], Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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]</code> || 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>]] || <code>Error</code> || <code>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]]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [96 / 120]<div class="mw-collapsible-content"><code>{Plus[QHypergeometricPFQ[{-1.5, Complex[-0.5773502691896257, -0.33333333333333326]} <- {Complex[-0.8660254037844387, -0.49999999999999994], -0.5}, Complex[0.8660254037844387, 0.49999999999999994], 0.5], Times[-1.0, Power[QPochhammer[-0.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[0.28867513459481287, 0.16666666666666663], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], QPochhammer[0.75, Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]]]], {Rule[a, -1.5], Rule[b, -0.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Indeterminate <- {Rule[a, -1.5], Rule[b, -0.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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}]}]]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><code>{Plus[QHypergeometricPFQ[{2.25, 2.25} <- {Complex[2.173333109150404, 0.5823428514806717], Complex[-2.173333109150404, -0.5823428514806717]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.8660254037844387, -0.49999999999999994]], Times[-1.0, Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], -1], Power[QPochhammer[Complex[1.948557158514987, 1.1249999999999998], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], 2], Power[QPochhammer[Complex[4.384253606658721, 2.5312499999999996], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], -1]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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]])</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [260 / 300]<div class="mw-collapsible-content"><code>{Plus[QHypergeometricPFQ[{1.0, 2.25} <- {-1.5, Complex[-1.299038105676658, -0.7499999999999999]}, Complex[0.5000000000000001, 0.8660254037844386], Complex[0.8660254037844387, 0.49999999999999994]], Times[-0.5, Power[QPochhammer[-1.5, Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], -1], Power[QPochhammer[Complex[-1.299038105676658, -0.7499999999999999], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], -1], QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], Plus[0.0, Times[QPochhammer[-1.0, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[1.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]]], QPochhammer[2.25, Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Indeterminate <- {Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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)}]}]]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [196 / 300]<div class="mw-collapsible-content"><code>{Plus[0.0, QHypergeometricPFQ[{-1.5, -1.5, Complex[0.8660254037844387, -0.49999999999999994]} <- {-1.5, -1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, -1.5, Complex[0.5000000000000001, -0.8660254037844386]} <- {-1.5, Complex[-1.299038105676658, 0.7499999999999999]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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}]}]]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[0.0, QHypergeometricPFQ[{-1.5, -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[QHypergeometricPFQ[{Complex[-1.5, 0.0], Complex[-1.5, 0.0], Complex[-1.5, 0.0]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Power[QPochhammer[-1.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], 3], Power[QPochhammer[Complex[-1.5, 0.0], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -3]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[f, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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}]}]]</code> || 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>]] || <code>Error</code> || <code>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)}]}]]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [248 / 300]<div class="mw-collapsible-content"><code>{Plus[QHypergeometricPFQ[{-1.5, Complex[0.6123724356957944, -1.0606601717798212], -1.5, -1.5} <- {Complex[0.0, -1.224744871391589], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.27216552697590857, 0.4714045207910316]], Times[-1.0, QPochhammer[Complex[-1.299038105676658, -0.7499999999999999], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[-0.6123724356957944, 1.0606601717798212], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[-0.5773502691896257, -0.33333333333333326], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[-0.27216552697590857, 0.4714045207910316], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], Power[QPochhammer[Complex[0.4082482904638629, -0.7071067811865475], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], 2], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -2]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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)}]}]]</code> || 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>]] || <code>Error</code> || <code>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}]}]]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [296 / 300]<div class="mw-collapsible-content"><code>{Plus[0.0, QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], Complex[0.5000000000000001, 0.8660254037844386], -1.5, 1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[2.25, 0.0], Complex[-0.8660254037844387, -0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[c, -1.5], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], Complex[0.0, 1.0], -1.5, 1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[2.25, 0.0], Complex[-0.8660254037844387, -0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[-1.0, QPochhammer[Complex[-0.49999999999999994, 0.8660254037844387], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], QPochhammer[Complex[3.3306690738754696*^-16, 2.25], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], QPochhammer[Complex[0.8660254037844387, -0.49999999999999994], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[1.1250000000000004, -1.9485571585149868], Complex[0.5000000000000001, 0.8660254037844386], DirectedInfinity[1]], Power[QPochhammer[Complex[2.25, 0.0], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]]], {Rule[c, -1.5], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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}]}]]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [246 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[-1.299038105676658, -0.7499999999999999], Complex[1.1250000000000002, 1.9485571585149868], Complex[0.5000000000000001, -0.8660254037844386]} <- {-1.5, Complex[-1.299038105676658, -0.7499999999999999], Complex[1.1250000000000002, 1.9485571585149868]}, Complex[0.5000000000000001, 0.8660254037844386], Complex[0.5000000000000001, 0.8660254037844386]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[-1.299038105676658, -0.7499999999999999], Complex[-1.1249999999999996, 1.948557158514987], Complex[-0.4999999999999998, -0.8660254037844387]} <- {-1.5, Complex[-1.299038105676658, -0.7499999999999999], Complex[1.1250000000000002, 1.9485571585149868]}, Complex[0.5000000000000001, 0.8660254037844386], Complex[0.5000000000000001, 0.8660254037844386]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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))]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[-1.299038105676658, -0.7499999999999999], 2.25, Complex[0.5000000000000001, -0.8660254037844386]} <- {-1.5, Complex[-1.299038105676658, -0.7499999999999999], 2.25}, Complex[0.5000000000000001, 0.8660254037844386], Complex[0.5000000000000001, 0.8660254037844386]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{-1.5, Complex[-1.299038105676658, -0.7499999999999999], Complex[1.1250000000000002, 1.9485571585149868], Complex[-0.4999999999999998, -0.8660254037844387]} <- {-1.5, Complex[-1.299038105676658, -0.7499999999999999], 2.25}, Complex[0.5000000000000001, 0.8660254037844386], Complex[0.5000000000000001, 0.8660254037844386]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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}]}]]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[14.55021169820366, 2.220446049250313*^-16], QHypergeometricPFQ[{-1.5, Complex[-0.6123724356957944, 1.0606601717798212], Complex[0.6123724356957944, -1.0606601717798212], -1.5, -1.5, Complex[0.8660254037844387, -0.49999999999999994]} <- {Complex[0.0, 1.224744871391589], Complex[0.0, -1.224744871391589], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.7500000000000002, -1.299038105676658]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.33333333333333337, -0.5773502691896257]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[-46.07567037764495, -8.881784197001252*^-15], QHypergeometricPFQ[{-1.5, Complex[-0.6123724356957944, 1.0606601717798212], Complex[0.6123724356957944, -1.0606601717798212], -1.5, -1.5, Complex[0.5000000000000001, -0.8660254037844386]} <- {Complex[0.0, 1.224744871391589], Complex[0.0, -1.224744871391589], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.0, -1.5]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.0, -0.6666666666666666]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>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)</code> || <code>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)</code> || Failure || Error || Error || 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>]] || <code>Error</code> || <code>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]</code> || 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>]] || <code>Error</code> || <code>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]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [290 / 300]<div class="mw-collapsible-content"><code>{Plus[0.0, QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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]</code> || 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>]] || <code>Error</code> || <code>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]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [294 / 300]<div class="mw-collapsible-content"><code>{Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [294 / 300]<div class="mw-collapsible-content"><code>{Plus[0.0, QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Complex[0.0, 0.0], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5} <- {-1.5}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [264 / 300]<div class="mw-collapsible-content"><code>{Plus[QHypergeometricPFQ[{-1.5, -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.14814814814814822, -0.25660011963983365]], Times[-1.0, QHypergeometricPFQ[{-1.5, Complex[-0.5773502691896257, -0.33333333333333326], Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.2222222222222223, 0.38490017945975047]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.5773502691896257, -0.33333333333333326]], QPochhammer[Complex[-0.5773502691896257, -0.33333333333333326], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[-0.14814814814814822, -0.25660011963983365], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[0.2222222222222223, 0.38490017945975047], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Plus[QHypergeometricPFQ[{-1.5, -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.14814814814814822, -0.25660011963983365]], Times[-1.0, QHypergeometricPFQ[{Complex[-0.5773502691896257, -0.33333333333333326], Complex[-0.5773502691896257, -0.33333333333333326], Complex[-0.14814814814814822, -0.25660011963983365]}, {Complex[0.2222222222222223, 0.38490017945975047], Complex[0.2222222222222223, 0.38490017945975047]}, Complex[0.8660254037844387, 0.49999999999999994], -1.5], QPochhammer[-1.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[-0.14814814814814822, -0.25660011963983365], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], Power[QPochhammer[Complex[0.2222222222222223, 0.38490017945975047], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], 2], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -2]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [188 / 300]<div class="mw-collapsible-content"><code>{Plus[QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[Complex[-3.573557158514987, -1.2075317547305489], QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], Complex[-0.5773502691896257, -0.33333333333333326], Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.2222222222222223, 0.38490017945975047]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[Complex[-8.437338913245533, -3.8821710443592976], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], Complex[-0.5773502691896257, -0.33333333333333326], Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.2222222222222223, 0.38490017945975047]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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]]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [228 / 300]<div class="mw-collapsible-content"><code>{Plus[QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[Complex[0.2499999999999999, 4.665063509461097], QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[-1.299038105676658, 0.7499999999999999]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-1.5, 0.0]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[Complex[10.037658773652746, -1.7075317547305477], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5, Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.7500000000000001, 1.2990381056766578]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-1.5, 0.0]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [198 / 300]<div class="mw-collapsible-content"><code>{Plus[QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[1.1102230246251565*^-16, 0.4444444444444444]], Times[Complex[-0.16666666666666663, -3.1100423396407315], QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[-1.299038105676658, 0.7499999999999999]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.2222222222222221, 0.38490017945975064]], Times[Complex[4.461181677178999, -0.7589030021024659], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5, Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.7500000000000001, 1.2990381056766578]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [210 / 300]<div class="mw-collapsible-content"><code>{Plus[QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[Complex[-14.466878364870325, 1.5550211698203658], QHypergeometricPFQ[{Complex[0.8660254037844387, -0.49999999999999994], -1.5, Complex[1.1250000000000004, -1.9485571585149868]}, {Complex[-1.299038105676658, 0.7499999999999999], Complex[-1.299038105676658, 0.7499999999999999]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Times[Complex[-43.48396842794434, 15.235218754810454], QHypergeometricPFQ[{Complex[0.5000000000000001, -0.8660254037844386], -1.5, Complex[6.661338147750939*^-16, -2.25]}, {Complex[-0.7500000000000001, 1.2990381056766578], Complex[-0.7500000000000001, 1.2990381056766578]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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]]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [246 / 300]<div class="mw-collapsible-content"><code>{Plus[0.0, QHypergeometricPFQ[{-1.5, -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.14814814814814822, -0.25660011963983365]], Times[QHypergeometricPFQ[{Complex[-1.5, 0.0], Complex[-1.5, 0.0], Complex[-1.5, 0.0]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.14814814814814822, -0.25660011963983365]], Power[QPochhammer[-1.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], 2], Power[QPochhammer[Complex[-1.5, 0.0], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -2], Power[QPochhammer[Complex[2.25, 0.0], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[2.25, 2.220446049250313*^-16], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [246 / 300]<div class="mw-collapsible-content"><code>{Plus[QHypergeometricPFQ[{-1.5, -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.14814814814814822, -0.25660011963983365]], Times[-1.0, QHypergeometricPFQ[{Complex[-0.5773502691896257, -0.33333333333333326], -1.5, -1.5}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[2.25, 0.0]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Power[QPochhammer[Complex[-0.5773502691896257, -0.33333333333333326], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], 2], Power[QPochhammer[Complex[0.3849001794597505, 0.22222222222222218], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]], Times[-1.0, QHypergeometricPFQ[{Complex[-0.5773502691896257, -0.33333333333333326], Complex[-0.5773502691896257, -0.33333333333333326], Complex[-0.14814814814814822, -0.25660011963983365]}, {Complex[0.2222222222222223, 0.38490017945975047], Complex[0.2222222222222223, 0.38490017945975047]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Power[QPochhammer[-1.5, Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], 2], QPochhammer[Complex[-0.5773502691896257, -0.33333333333333326], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[-0.14814814814814822, -0.25660011963983365], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[0.2222222222222223, 0.38490017945975047], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -2], Power[QPochhammer[Complex[1.948557158514987, -1.1249999999999998], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Indeterminate <- {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[q, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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]</code> || 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>]] || <code>Error</code> || <code>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]</code> || 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>]] || <code>Error</code> || <code>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]]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [240 / 300]<div class="mw-collapsible-content"><code>{Plus[Times[Complex[0.9356921938165307, -5.551115123125783*^-17], QHypergeometricPFQ[{Complex[-0.5773502691896257, -0.33333333333333326], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, -0.49999999999999994]} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.5773502691896257, -0.3333333333333332]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], Times[-1.0, QHypergeometricPFQ[{-1.5, Complex[-0.6123724356957944, 1.0606601717798212], Complex[0.6123724356957944, -1.0606601717798212], -1.5, -1.5, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, -0.49999999999999994]}, {Complex[0.0, 1.224744871391589], Complex[0.0, -1.224744871391589], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[-1.5, 0.0], Complex[-1.5, 0.0], Complex[-0.7500000000000002, -1.299038105676658]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844386, 0.5000000000000002]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Times[Complex[0.8717526973154065, 0.006872752237161106], QHypergeometricPFQ[{Complex[-0.5773502691896257, -0.33333333333333326], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.5000000000000001, -0.8660254037844386]} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.6666666666666666, 0.0]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]], Times[-1.0, QHypergeometricPFQ[{-1.5, Complex[-0.6123724356957944, 1.0606601717798212], Complex[0.6123724356957944, -1.0606601717798212], -1.5, -1.5, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.5000000000000001, -0.8660254037844386]}, {Complex[0.0, 1.224744871391589], Complex[0.0, -1.224744871391589], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[-1.5, 0.0], Complex[-1.5, 0.0], Complex[0.0, -1.5]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.5, 0.8660254037844386]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[e, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>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]</code> || 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>]] || <code>Error</code> || <code>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]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [298 / 300]<div class="mw-collapsible-content"><code>{Plus[QHypergeometricPFQ[{-1.5, -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[-0.33333333333333337, -0.5773502691896257]], Times[-1.0, QHypergeometricPFQ[{Complex[0.0, 1.224744871391589], Complex[0.0, -1.224744871391589], Complex[0.31698729810778065, -1.1830127018922192], Complex[-0.31698729810778065, 1.1830127018922192], Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[-1.299038105676658, -0.7499999999999999], 1.0}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], QPochhammer[Complex[-1.299038105676658, -0.7499999999999999], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], Power[QPochhammer[Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[QHypergeometricPFQ[{-1.5, -1.5, -1.5} <- {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.5773502691896256, -0.3333333333333335]], Times[-1.0, QHypergeometricPFQ[{Complex[0.0, 1.224744871391589], Complex[0.0, -1.224744871391589], Complex[0.31698729810778065, -1.1830127018922192], Complex[-0.31698729810778065, 1.1830127018922192], Complex[-0.5773502691896257, -0.33333333333333326]}, {Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994], Complex[0.7499999999999997, -1.299038105676658], Complex[0.0, -1.0]}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], Power[QPochhammer[Complex[-0.4999999999999998, 0.8660254037844387], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]], -1], QPochhammer[Complex[0.7499999999999997, -1.299038105676658], Complex[0.8660254037844387, 0.49999999999999994], DirectedInfinity[1]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[c, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>Error</code> || <code>(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]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [284 / 300]<div class="mw-collapsible-content"><code>{Plus[Power[QHypergeometricPFQ[{-1.5, -1.5, Complex[1.948557158514987, 1.1249999999999998], Complex[1.948557158514987, -1.1249999999999998]} <- {Complex[2.173333109150404, 0.5823428514806717], Complex[-2.173333109150404, -0.5823428514806717], -2.25}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], 2], Times[-1.0, QHypergeometricPFQ[{2.25, 2.25, 2.25, Complex[1.948557158514987, 1.1249999999999998], Complex[1.948557158514987, -1.1249999999999998]}, {Complex[2.173333109150404, 0.5823428514806717], Complex[-2.173333109150404, -0.5823428514806717], -2.25, 5.0625}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Plus[Power[QHypergeometricPFQ[{-1.5, -1.5, Complex[-1.1249999999999996, 1.948557158514987], Complex[-1.1249999999999996, -1.948557158514987]} <- {Complex[2.173333109150404, 0.5823428514806717], Complex[-2.173333109150404, -0.5823428514806717], -2.25}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]], 2], Times[-1.0, QHypergeometricPFQ[{2.25, 2.25, 2.25, Complex[-1.1249999999999996, 1.948557158514987], Complex[-1.1249999999999996, -1.948557158514987]}, {Complex[2.173333109150404, 0.5823428514806717], Complex[-2.173333109150404, -0.5823428514806717], -2.25, 5.0625}, Complex[0.8660254037844387, 0.49999999999999994], Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[a, -1.5], Rule[b, -1.5], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[z, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</code><br></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>]] || <code>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)</code> || <code>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]</code> || Failure || Error || Error || 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>]] || <code>sum(alpha[n]*gamma[n], n = 0..infinity) = sum(beta[n]*delta[n], n = 0..infinity)</code> || <code>Sum[Subscript[\[Alpha], n]*Subscript[\[Gamma], n], {n, 0, Infinity}, GenerateConditions->None] == Sum[Subscript[\[Beta], n]*Subscript[\[Delta], n], {n, 0, Infinity}, GenerateConditions->None]</code> || 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>]] || <code>beta[n] = sum(alpha[j]*u[n - j]*v[n + j], j = 0..n)</code> || <code>Subscript[\[Beta], n] == Sum[Subscript[\[Alpha], j]*Subscript[u, n - j]*Subscript[v, n + j], {j, 0, n}, GenerateConditions->None]</code> || 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>]] || <code>gamma[n] = sum(delta[j]*u[j - n]*v[j + n], j = n..infinity)</code> || <code>Subscript[\[Gamma], n] == Sum[Subscript[\[Delta], j]*Subscript[u, j - n]*Subscript[v, j + n], {j, n, Infinity}, GenerateConditions->None]</code> || 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>]] || <code>beta[n] = sum((alpha[j])/(QPochhammer(q, q, n - j)*QPochhammer(a*q, q, n + j)), j = 0..n)</code> || <code>Subscript[\[Beta], n] == Sum[Divide[Subscript[\[Alpha], j],QPochhammer[q, q, n - j]*QPochhammer[a*q, q, n + j]], {j, 0, n}, GenerateConditions->None]</code> || Failure || Error || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[0.6508376433032488, -0.21856268949920582] <- {Rule[a, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[Subscript[α, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[β, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[0.8660402331469415, 0.20457300495175623] <- {Rule[a, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[β, 1.5], Rule[Subscript[α, j], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[β, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>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)</code> || <code>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]</code> || Failure || Error || 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>]] || <code>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))</code> || <code>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)]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><code>{Complex[5.814582562299427, -3.4240381056766607] <- {Rule[a, -1.5], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[α, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[-12.010896071760529, -4.7481964481437355] <- {Rule[a, -1.5], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 1.5], Rule[Subscript[α, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>beta[n] = (1)/(QPochhammer(q, q, n))</code> || <code>Subscript[\[Beta], n] == Divide[1,QPochhammer[q, q, n]]</code> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [297 / 300]<div class="mw-collapsible-content"><code>{Complex[0.3660254037844387, -1.366025403784439] <- {Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[β, 1.5], Rule[Subscript[β, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br><code>Complex[2.232050807568878, -0.8660254037844388] <- {Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[β, 1.5], Rule[Subscript[β, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}</code><br></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>]] || <code>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))</code> || <code>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]]</code> || Error || Failure || - || <div class="toccolours mw-collapsible mw-collapsed">Failed [26 / 30]<div class="mw-collapsible-content"><code>{Plus[NIntegrate[Times[Power[t, -0.5], Power[QPochhammer[Times[-1, t], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], DirectedInfinity[1]], -1], QPochhammer[Times[Complex[-0.5000000000000001, -0.8660254037844386], t], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], DirectedInfinity[1]]] <- {t, 0, DirectedInfinity[1]}], Times[-3.1415926535897936, Power[QGamma[0.5, Complex[0.8660254037844387, 0.49999999999999994]], -1], QGamma[1.5, Complex[0.8660254037844387, 0.49999999999999994]]]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5], Rule[β, 1.5]}</code><br><code>Plus[-3.1415926535897936, NIntegrate[Times[Power[t, -0.5], Power[QPochhammer[Times[-1, t], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], DirectedInfinity[1]], -1], QPochhammer[Times[Complex[-0.8660254037844387, -0.49999999999999994], t], Power[E, Times[Complex[0, Rational[1, 6]], Pi]], DirectedInfinity[1]]] <- {t, 0, DirectedInfinity[1]}]], {Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[α, 0.5], Rule[β, 0.5]}</code><br></div></div>
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