Deprecated : $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372 DLMF:17.13.E1 - MaRDI portal
Statements
∫
-
c
d
(
-
q
x
/
c
;
q
)
∞
(
q
x
/
d
;
q
)
∞
(
-
a
x
/
c
;
q
)
∞
(
b
x
/
d
;
q
)
∞
d
q
x
=
(
1
-
q
)
(
q
;
q
)
∞
(
a
b
;
q
)
∞
c
d
(
-
c
/
d
;
q
)
∞
(
-
d
/
c
;
q
)
∞
(
a
;
q
)
∞
(
b
;
q
)
∞
(
c
+
d
)
(
-
b
c
/
d
;
q
)
∞
(
-
a
d
/
c
;
q
)
∞
,
superscript
subscript
𝑐
𝑑
q-Pochhammer-symbol
𝑞
𝑥
𝑐
𝑞
q-Pochhammer-symbol
𝑞
𝑥
𝑑
𝑞
q-Pochhammer-symbol
𝑎
𝑥
𝑐
𝑞
q-Pochhammer-symbol
𝑏
𝑥
𝑑
𝑞
q-differential
𝑞
𝑥
1
𝑞
q-Pochhammer-symbol
𝑞
𝑞
q-Pochhammer-symbol
𝑎
𝑏
𝑞
𝑐
𝑑
q-Pochhammer-symbol
𝑐
𝑑
𝑞
q-Pochhammer-symbol
𝑑
𝑐
𝑞
q-Pochhammer-symbol
𝑎
𝑞
q-Pochhammer-symbol
𝑏
𝑞
𝑐
𝑑
q-Pochhammer-symbol
𝑏
𝑐
𝑑
𝑞
q-Pochhammer-symbol
𝑎
𝑑
𝑐
𝑞
{\displaystyle{\displaystyle\int_{-c}^{d}\frac{\left(-qx/c;q\right)_{\infty}%
\left(qx/d;q\right)_{\infty}}{\left(-ax/c;q\right)_{\infty}\left(bx/d;q\right)%
_{\infty}}{\mathrm{d}}_{q}x=\frac{(1-q)\left(q;q\right)_{\infty}\left(ab;q%
\right)_{\infty}cd\left(-c/d;q\right)_{\infty}\left(-d/c;q\right)_{\infty}}{%
\left(a;q\right)_{\infty}\left(b;q\right)_{\infty}(c+d)\left(-bc/d;q\right)_{%
\infty}\left(-ad/c;q\right)_{\infty}},}}
∫
{\displaystyle{\displaystyle\int}}
(
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
