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DLMF:17.7.E3 - MaRDI portal
Statements
ϕ
2
2
(
c
2
/
b
2
,
b
2
c
,
c
q
;
q
2
,
q
)
=
1
2
(
b
2
,
q
;
q
2
)
∞
(
c
,
c
q
;
q
2
)
∞
(
(
c
/
b
;
q
)
∞
(
b
;
q
)
∞
+
(
-
c
/
b
;
q
)
∞
(
-
b
;
q
)
∞
)
.
q-hypergeometric-rphis
2
2
superscript
𝑐
2
superscript
𝑏
2
superscript
𝑏
2
𝑐
𝑐
𝑞
superscript
𝑞
2
𝑞
1
2
q-multiple-Pochhammer
superscript
𝑏
2
𝑞
superscript
𝑞
2
q-multiple-Pochhammer
𝑐
𝑐
𝑞
superscript
𝑞
2
q-Pochhammer-symbol
𝑐
𝑏
𝑞
q-Pochhammer-symbol
𝑏
𝑞
q-Pochhammer-symbol
𝑐
𝑏
𝑞
q-Pochhammer-symbol
𝑏
𝑞
{\displaystyle{\displaystyle{{}_{2}\phi_{2}}\left({\ifrac{c^{2}}{b^{2}},b^{2}%
\atop c,cq};q^{2},q\right)=\frac{1}{2}\frac{\left(b^{2},q;q^{2}\right)_{\infty%
}}{\left(c,cq;q^{2}\right)_{\infty}}{\left(\frac{\left(c/b;q\right)_{\infty}}{%
\left(b;q\right)_{\infty}}+\frac{\left(-c/b;q\right)_{\infty}}{\left(-b;q%
\right)_{\infty}}\right)}.}}
(
a
;
q
)
n
q-Pochhammer-symbol
𝑎
𝑞
𝑛
{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
ϕ
s
r
+
1
(
a
0
,
…
,
a
r
;
b
1
,
…
,
b
s
;
q
,
z
)
q-hypergeometric-rphis
𝑟
1
𝑠
subscript
𝑎
0
…
subscript
𝑎
𝑟
subscript
𝑏
1
…
subscript
𝑏
𝑠
𝑞
𝑧
{\displaystyle{\displaystyle{{}_{\NVar{r+1}}\phi_{\NVar{s}}}\left(\NVar{a_{0},%
\dots,a_{r}};\NVar{b_{1},\dots,b_{s}};\NVar{q},\NVar{z}\right)}}
(
a
1
,
a
2
,
…
,
a
r
;
q
)
n
q-multiple-Pochhammer
subscript
𝑎
1
subscript
𝑎
2
…
subscript
𝑎
𝑟
𝑞
𝑛
{\displaystyle{\displaystyle\left(\NVar{a_{1},a_{2},\dots,a_{r}};\NVar{q}%
\right)_{\NVar{n}}}}
q
𝑞
{\displaystyle{\displaystyle q}}
Identifiers