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Statements
ϕ
1
2
(
a
,
b
c
;
q
,
z
)
=
(
a
b
z
/
c
,
q
/
c
;
q
)
∞
(
a
z
/
c
,
q
/
a
;
q
)
∞
ϕ
1
2
(
c
/
a
,
c
q
/
(
a
b
z
)
c
q
/
(
a
z
)
;
q
,
b
q
/
c
)
-
(
b
,
q
/
c
,
c
/
a
,
a
z
/
q
,
q
2
/
(
a
z
)
;
q
)
∞
(
c
/
q
,
b
q
/
c
,
q
/
a
,
a
z
/
c
,
c
q
/
(
a
z
)
;
q
)
∞
ϕ
1
2
(
a
q
/
c
,
b
q
/
c
q
2
/
c
;
q
,
z
)
,
q-hypergeometric-rphis
2
1
𝑎
𝑏
𝑐
𝑞
𝑧
q-multiple-Pochhammer
𝑎
𝑏
𝑧
𝑐
𝑞
𝑐
𝑞
q-multiple-Pochhammer
𝑎
𝑧
𝑐
𝑞
𝑎
𝑞
q-hypergeometric-rphis
2
1
𝑐
𝑎
𝑐
𝑞
𝑎
𝑏
𝑧
𝑐
𝑞
𝑎
𝑧
𝑞
𝑏
𝑞
𝑐
q-multiple-Pochhammer
𝑏
𝑞
𝑐
𝑐
𝑎
𝑎
𝑧
𝑞
superscript
𝑞
2
𝑎
𝑧
𝑞
q-multiple-Pochhammer
𝑐
𝑞
𝑏
𝑞
𝑐
𝑞
𝑎
𝑎
𝑧
𝑐
𝑐
𝑞
𝑎
𝑧
𝑞
q-hypergeometric-rphis
2
1
𝑎
𝑞
𝑐
𝑏
𝑞
𝑐
superscript
𝑞
2
𝑐
𝑞
𝑧
{\displaystyle{\displaystyle{{}_{2}\phi_{1}}\left({a,b\atop c};q,z\right)=%
\frac{\left(abz/c,q/c;q\right)_{\infty}}{\left(az/c,q/a;q\right)_{\infty}}{{}_%
{2}\phi_{1}}\left({c/a,cq/(abz)\atop cq/(az)};q,bq/c\right)-\frac{\left(b,q/c,%
c/a,az/q,q^{2}/(az);q\right)_{\infty}}{\left(c/q,bq/c,q/a,az/c,cq/(az);q\right%
)_{\infty}}{{}_{2}\phi_{1}}\left({aq/c,bq/c\atop q^{2}/c};q,z\right),}}
|
z
|
<
1
,
|
b
q
|
<
|
c
|
formulae-sequence
𝑧
1
𝑏
𝑞
𝑐
{\displaystyle{\displaystyle|z|<1,|bq|<|c|}}
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}}
z
𝑧
{\displaystyle{\displaystyle z}}
Identifiers
