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Statements
q
(
1
-
a
c
)
ϕ
1
2
(
a
/
q
,
b
c
;
q
,
z
)
+
(
1
-
a
)
(
1
-
a
b
z
c
)
ϕ
1
2
(
a
q
,
b
c
;
q
,
z
)
=
(
1
+
q
-
a
-
a
q
c
+
a
2
z
c
-
a
b
z
c
)
ϕ
1
2
(
a
,
b
c
;
q
,
z
)
,
𝑞
1
𝑎
𝑐
q-hypergeometric-rphis
2
1
𝑎
𝑞
𝑏
𝑐
𝑞
𝑧
1
𝑎
1
𝑎
𝑏
𝑧
𝑐
q-hypergeometric-rphis
2
1
𝑎
𝑞
𝑏
𝑐
𝑞
𝑧
1
𝑞
𝑎
𝑎
𝑞
𝑐
superscript
𝑎
2
𝑧
𝑐
𝑎
𝑏
𝑧
𝑐
q-hypergeometric-rphis
2
1
𝑎
𝑏
𝑐
𝑞
𝑧
{\displaystyle{\displaystyle q\left(1-\frac{a}{c}\right){{}_{2}\phi_{1}}\left(%
{a/q,b\atop c};q,z\right)+(1-a)\left(1-\frac{abz}{c}\right){{}_{2}\phi_{1}}%
\left({aq,b\atop c};q,z\right)=\left(1+q-a-\frac{aq}{c}+\frac{a^{2}z}{c}-\frac%
{abz}{c}\right){{}_{2}\phi_{1}}\left({a,b\atop c};q,z\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
