MaRDI QID Q6130
Digital Library of Mathematical Functions ID 17.9.E7
ϕ
2
3
(
a
,
b
,
c
d
,
e
;
q
,
d
e
/
(
a
b
c
)
)
=
(
b
,
d
e
/
(
a
b
)
,
d
e
/
(
b
c
)
;
q
)
∞
(
d
,
e
,
d
e
/
(
a
b
c
)
;
q
)
∞
ϕ
2
3
(
d
/
b
,
e
/
b
,
d
e
/
(
a
b
c
)
d
e
/
(
a
b
)
,
d
e
/
(
b
c
)
;
q
,
b
)
,
q-hypergeometric-rphis
3
2
𝑎
𝑏
𝑐
𝑑
𝑒
𝑞
𝑑
𝑒
𝑎
𝑏
𝑐
q-multiple-Pochhammer
𝑏
𝑑
𝑒
𝑎
𝑏
𝑑
𝑒
𝑏
𝑐
𝑞
q-multiple-Pochhammer
𝑑
𝑒
𝑑
𝑒
𝑎
𝑏
𝑐
𝑞
q-hypergeometric-rphis
3
2
𝑑
𝑏
𝑒
𝑏
𝑑
𝑒
𝑎
𝑏
𝑐
𝑑
𝑒
𝑎
𝑏
𝑑
𝑒
𝑏
𝑐
𝑞
𝑏
{\displaystyle{\displaystyle{{}_{3}\phi_{2}}\left({a,b,c\atop d,e};q,de/(abc)%
\right)=\frac{\left(b,de/(ab),de/(bc);q\right)_{\infty}}{\left(d,e,de/(abc);q%
\right)_{\infty}}\*{{}_{3}\phi_{2}}\left({d/b,e/b,de/(abc)\atop de/(ab),de/(bc%
)};q,b\right),}}
Constraint(s) Symbols List
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}}
Resources that cite this formula No records found.
