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Statements
B
q
(
a
,
b
)
=
∫
0
1
t
a
-
1
(
t
q
;
q
)
∞
(
t
q
b
;
q
)
∞
d
q
t
,
q-Beta
𝑞
𝑎
𝑏
superscript
subscript
0
1
superscript
𝑡
𝑎
1
q-Pochhammer-symbol
𝑡
𝑞
𝑞
q-Pochhammer-symbol
𝑡
superscript
𝑞
𝑏
𝑞
q-differential
𝑞
𝑡
{\displaystyle{\displaystyle\mathrm{B}_{q}\left(a,b\right)=\int_{0}^{1}\frac{t%
^{a-1}\left(tq;q\right)_{\infty}}{\left(tq^{b};q\right)_{\infty}}{\mathrm{d}}_%
{q}t,}}
ℜ
a
>
0
𝑎
0
{\displaystyle{\displaystyle\Re a>0}}
ℜ
b
>
0
𝑏
0
{\displaystyle{\displaystyle\Re b>0}}
0
<
q
<
1
0
𝑞
1
{\displaystyle{\displaystyle 0<q<1}}
ℜ
a
>
0
𝑎
0
{\displaystyle{\displaystyle\Re a>0}}
ℜ
b
>
0
𝑏
0
{\displaystyle{\displaystyle\Re b>0}}
∫
{\displaystyle{\displaystyle\int}}
B
q
(
a
,
b
)
q-Beta
𝑞
𝑎
𝑏
{\displaystyle{\displaystyle\mathrm{B}_{\NVar{q}}\left(\NVar{a},\NVar{b}\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}}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
q
𝑞
{\displaystyle{\displaystyle q}}
a
𝑎
{\displaystyle{\displaystyle a}}
b
𝑏
{\displaystyle{\displaystyle b}}
Identifiers
