DLMF:5.18.E12
(Q2199)
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No description defined
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English
DLMF:5.18.E12
No description defined
Statements
Defining formula
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,}}
0 references
DLMF id
DLMF:5.18.E12
0 references
constraint
ℜ
a
>
0
𝑎
0
{\displaystyle{\displaystyle\Re a>0}}
0 references
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