MaRDI QID Q6138
Digital Library of Mathematical Functions ID 17.9.E15
(
a
q
,
a
q
/
(
d
e
)
;
q
)
n
(
a
q
/
d
,
a
q
/
e
;
q
)
n
ϕ
3
4
(
a
q
/
(
b
c
)
,
d
,
e
,
q
-
n
a
q
/
b
,
a
q
/
c
,
d
e
q
-
n
/
a
;
q
,
q
)
=
ϕ
7
8
(
a
,
q
a
1
2
,
-
q
a
1
2
,
b
,
c
,
d
,
e
,
q
-
n
a
1
2
,
-
a
1
2
,
a
q
/
b
,
a
q
/
c
,
a
q
/
d
,
a
q
/
e
,
a
q
n
+
1
;
q
,
a
2
q
2
+
n
b
c
d
e
)
.
q-multiple-Pochhammer
𝑎
𝑞
𝑎
𝑞
𝑑
𝑒
𝑞
𝑛
q-multiple-Pochhammer
𝑎
𝑞
𝑑
𝑎
𝑞
𝑒
𝑞
𝑛
q-hypergeometric-rphis
4
3
𝑎
𝑞
𝑏
𝑐
𝑑
𝑒
superscript
𝑞
𝑛
𝑎
𝑞
𝑏
𝑎
𝑞
𝑐
𝑑
𝑒
superscript
𝑞
𝑛
𝑎
𝑞
𝑞
q-hypergeometric-rphis
8
7
𝑎
𝑞
superscript
𝑎
1
2
𝑞
superscript
𝑎
1
2
𝑏
𝑐
𝑑
𝑒
superscript
𝑞
𝑛
superscript
𝑎
1
2
superscript
𝑎
1
2
𝑎
𝑞
𝑏
𝑎
𝑞
𝑐
𝑎
𝑞
𝑑
𝑎
𝑞
𝑒
𝑎
superscript
𝑞
𝑛
1
𝑞
superscript
𝑎
2
superscript
𝑞
2
𝑛
𝑏
𝑐
𝑑
𝑒
{\displaystyle{\displaystyle\frac{\left(aq,aq/(de);q\right)_{n}}{\left(aq/d,aq%
/e;q\right)_{n}}{{}_{4}\phi_{3}}\left({aq/(bc),d,e,q^{-n}\atop aq/b,aq/c,deq^{%
-n}/a};q,q\right)={{}_{8}\phi_{7}}\left({a,qa^{\frac{1}{2}},-qa^{\frac{1}{2}},%
b,c,d,e,q^{-n}\atop a^{\frac{1}{2}},-a^{\frac{1}{2}},aq/b,aq/c,aq/d,aq/e,aq^{n%
+1}};q,\frac{a^{2}q^{2+n}}{bcde}\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}}
n
𝑛
{\displaystyle{\displaystyle n}}
Resources that cite this formula No records found.
