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Statements
∫
-
c
d
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-
q
x
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c
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q
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∞
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q
x
/
d
;
q
)
∞
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x
q
α
/
c
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q
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∞
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x
q
β
/
d
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q
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∞
d
q
x
=
Γ
q
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α
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Γ
q
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β
)
Γ
q
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α
+
β
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c
d
c
+
d
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-
c
/
d
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q
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∞
(
-
d
/
c
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q
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∞
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-
q
β
c
/
d
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q
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∞
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-
q
α
d
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q
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∞
.
superscript
subscript
𝑐
𝑑
q-Pochhammer-symbol
𝑞
𝑥
𝑐
𝑞
q-Pochhammer-symbol
𝑞
𝑥
𝑑
𝑞
q-Pochhammer-symbol
𝑥
superscript
𝑞
𝛼
𝑐
𝑞
q-Pochhammer-symbol
𝑥
superscript
𝑞
𝛽
𝑑
𝑞
q-differential
𝑞
𝑥
q-Gamma
𝑞
𝛼
q-Gamma
𝑞
𝛽
q-Gamma
𝑞
𝛼
𝛽
𝑐
𝑑
𝑐
𝑑
q-Pochhammer-symbol
𝑐
𝑑
𝑞
q-Pochhammer-symbol
𝑑
𝑐
𝑞
q-Pochhammer-symbol
superscript
𝑞
𝛽
𝑐
𝑑
𝑞
q-Pochhammer-symbol
superscript
𝑞
𝛼
𝑑
𝑐
𝑞
{\displaystyle{\displaystyle\int_{-c}^{d}\frac{\left(-qx/c;q\right)_{\infty}%
\left(qx/d;q\right)_{\infty}}{\left(-xq^{\alpha}/c;q\right)_{\infty}\left(xq^{%
\beta}/d;q\right)_{\infty}}{\mathrm{d}}_{q}x=\frac{\Gamma_{q}\left(\alpha%
\right)\Gamma_{q}\left(\beta\right)}{\Gamma_{q}\left(\alpha+\beta\right)}\frac%
{cd}{c+d}\frac{\left(-c/d;q\right)_{\infty}\left(-d/c;q\right)_{\infty}}{\left%
(-q^{\beta}c/d;q\right)_{\infty}\left(-q^{\alpha}d/c;q\right)_{\infty}}.}}
∫
{\displaystyle{\displaystyle\int}}
Γ
q
(
z
)
q-Gamma
𝑞
𝑧
{\displaystyle{\displaystyle\Gamma_{\NVar{q}}\left(\NVar{z}\right)}}
(
a
;
q
)
n
q-Pochhammer-symbol
𝑎
𝑞
𝑛
{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
d
q
x
q-differential
𝑞
𝑥
{\displaystyle{\displaystyle{\mathrm{d}}_{\NVar{q}}\NVar{x}}}
q
𝑞
{\displaystyle{\displaystyle q}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
