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Statements
(
ϕ
3
4
(
a
,
b
,
a
b
z
,
a
b
/
z
a
b
q
1
2
,
-
a
b
q
1
2
,
-
a
b
;
q
,
q
)
)
2
=
ϕ
4
5
(
a
2
,
b
2
,
a
b
,
a
b
z
,
a
b
/
z
a
b
q
1
2
,
-
a
b
q
1
2
,
-
a
b
,
a
2
b
2
;
q
,
q
)
,
superscript
q-hypergeometric-rphis
4
3
𝑎
𝑏
𝑎
𝑏
𝑧
𝑎
𝑏
𝑧
𝑎
𝑏
superscript
𝑞
1
2
𝑎
𝑏
superscript
𝑞
1
2
𝑎
𝑏
𝑞
𝑞
2
q-hypergeometric-rphis
5
4
superscript
𝑎
2
superscript
𝑏
2
𝑎
𝑏
𝑎
𝑏
𝑧
𝑎
𝑏
𝑧
𝑎
𝑏
superscript
𝑞
1
2
𝑎
𝑏
superscript
𝑞
1
2
𝑎
𝑏
superscript
𝑎
2
superscript
𝑏
2
𝑞
𝑞
{\displaystyle{\displaystyle\left({{}_{4}\phi_{3}}\left({a,b,abz,ab/z\atop abq%
^{\frac{1}{2}},-abq^{\frac{1}{2}},-ab};q,q\right)\right)^{2}={{}_{5}\phi_{4}}%
\left({a^{2},b^{2},ab,abz,ab/z\atop abq^{\frac{1}{2}},-abq^{\frac{1}{2}},-ab,a%
^{2}b^{2}};q,q\right),}}
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)}}
q
𝑞
{\displaystyle{\displaystyle q}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
