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Statements
ϕ
3
4
(
q
-
n
,
a
q
n
,
c
,
-
c
(
a
q
)
1
2
,
-
(
a
q
)
1
2
,
c
2
;
q
,
q
)
=
{
0
,
n
odd,
c
n
(
q
,
a
q
/
c
2
;
q
2
)
n
/
2
(
a
q
,
c
2
q
;
q
2
)
n
/
2
,
n
even.
q-hypergeometric-rphis
4
3
superscript
𝑞
𝑛
𝑎
superscript
𝑞
𝑛
𝑐
𝑐
superscript
𝑎
𝑞
1
2
superscript
𝑎
𝑞
1
2
superscript
𝑐
2
𝑞
𝑞
cases
0
n
odd,
superscript
𝑐
𝑛
q-multiple-Pochhammer
𝑞
𝑎
𝑞
superscript
𝑐
2
superscript
𝑞
2
𝑛
2
q-multiple-Pochhammer
𝑎
𝑞
superscript
𝑐
2
𝑞
superscript
𝑞
2
𝑛
2
n
even.
{\displaystyle{\displaystyle{{}_{4}\phi_{3}}\left({q^{-n},aq^{n},c,-c\atop(aq)%
^{\frac{1}{2}},-(aq)^{\frac{1}{2}},c^{2}};q,q\right)=\begin{cases}0,&\mbox{$n$%
odd,}\\
\dfrac{c^{n}\left(q,aq/c^{2};q^{2}\right)_{n/2}}{\left(aq,c^{2}q;q^{2}\right)_%
{n/2}},&\mbox{$n$ even.}\end{cases}}}
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}}
n
𝑛
{\displaystyle{\displaystyle n}}
Identifiers
