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Statements
ϕ
s
r
+
1
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a
0
,
a
1
,
a
2
,
…
,
a
r
b
1
,
b
2
,
…
,
b
s
;
q
,
z
)
=
ϕ
s
r
+
1
(
a
0
,
a
1
,
…
,
a
r
;
b
1
,
b
2
,
…
,
b
s
;
q
,
z
)
=
∑
n
=
0
∞
(
a
0
;
q
)
n
(
a
1
;
q
)
n
⋯
(
a
r
;
q
)
n
(
q
;
q
)
n
(
b
1
;
q
)
n
⋯
(
b
s
;
q
)
n
(
(
-
1
)
n
q
(
n
2
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)
s
-
r
z
n
.
q-hypergeometric-rphis
𝑟
1
𝑠
subscript
𝑎
0
subscript
𝑎
1
subscript
𝑎
2
…
subscript
𝑎
𝑟
subscript
𝑏
1
subscript
𝑏
2
…
subscript
𝑏
𝑠
𝑞
𝑧
q-hypergeometric-rphis
𝑟
1
𝑠
subscript
𝑎
0
subscript
𝑎
1
…
subscript
𝑎
𝑟
subscript
𝑏
1
subscript
𝑏
2
…
subscript
𝑏
𝑠
𝑞
𝑧
superscript
subscript
𝑛
0
q-Pochhammer-symbol
subscript
𝑎
0
𝑞
𝑛
q-Pochhammer-symbol
subscript
𝑎
1
𝑞
𝑛
⋯
q-Pochhammer-symbol
subscript
𝑎
𝑟
𝑞
𝑛
q-Pochhammer-symbol
𝑞
𝑞
𝑛
q-Pochhammer-symbol
subscript
𝑏
1
𝑞
𝑛
⋯
q-Pochhammer-symbol
subscript
𝑏
𝑠
𝑞
𝑛
superscript
superscript
1
𝑛
superscript
𝑞
binomial
𝑛
2
𝑠
𝑟
superscript
𝑧
𝑛
{\displaystyle{\displaystyle{{}_{r+1}\phi_{s}}\left({a_{0},a_{1},a_{2},\dots,a%
_{r}\atop b_{1},b_{2},\dots,b_{s}};q,z\right)={{}_{r+1}\phi_{s}}\left(a_{0},a_%
{1},\dots,a_{r};b_{1},b_{2},\dots,b_{s};q,z\right)=\sum_{n=0}^{\infty}\frac{%
\left(a_{0};q\right)_{n}\left(a_{1};q\right)_{n}\cdots\left(a_{r};q\right)_{n}%
}{\left(q;q\right)_{n}\left(b_{1};q\right)_{n}\cdots\left(b_{s};q\right)_{n}}%
\*\left((-1)^{n}q^{\genfrac{(}{)}{0.0pt}{}{n}{2}}\right)^{s-r}z^{n}.}}
(
m
n
)
binomial
𝑚
𝑛
{\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
(
a
;
q
)
n
q-Pochhammer-symbol
𝑎
𝑞
𝑛
{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
q
𝑞
{\displaystyle{\displaystyle q}}
n
𝑛
{\displaystyle{\displaystyle n}}
r
𝑟
{\displaystyle{\displaystyle r}}
s
𝑠
{\displaystyle{\displaystyle s}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
