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Statements
ϕ
3
4
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q
-
n
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a
,
b
,
c
d
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e
,
f
;
q
,
q
)
=
(
e
/
a
,
f
/
a
;
q
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n
(
e
,
f
;
q
)
n
a
n
ϕ
3
4
(
q
-
n
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a
,
d
/
b
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d
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c
d
,
a
q
1
-
n
/
e
,
a
q
1
-
n
/
f
;
q
,
q
)
=
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a
,
e
f
/
(
a
b
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,
e
f
/
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a
c
)
;
q
)
n
(
e
,
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,
e
f
/
(
a
b
c
)
;
q
)
n
ϕ
3
4
(
q
-
n
,
e
/
a
,
f
/
a
,
e
f
/
(
a
b
c
)
e
f
/
(
a
b
)
,
e
f
/
(
a
c
)
,
q
1
-
n
/
a
;
q
,
q
)
.
q-hypergeometric-rphis
4
3
superscript
𝑞
𝑛
𝑎
𝑏
𝑐
𝑑
𝑒
𝑓
𝑞
𝑞
q-multiple-Pochhammer
𝑒
𝑎
𝑓
𝑎
𝑞
𝑛
q-multiple-Pochhammer
𝑒
𝑓
𝑞
𝑛
superscript
𝑎
𝑛
q-hypergeometric-rphis
4
3
superscript
𝑞
𝑛
𝑎
𝑑
𝑏
𝑑
𝑐
𝑑
𝑎
superscript
𝑞
1
𝑛
𝑒
𝑎
superscript
𝑞
1
𝑛
𝑓
𝑞
𝑞
q-multiple-Pochhammer
𝑎
𝑒
𝑓
𝑎
𝑏
𝑒
𝑓
𝑎
𝑐
𝑞
𝑛
q-multiple-Pochhammer
𝑒
𝑓
𝑒
𝑓
𝑎
𝑏
𝑐
𝑞
𝑛
q-hypergeometric-rphis
4
3
superscript
𝑞
𝑛
𝑒
𝑎
𝑓
𝑎
𝑒
𝑓
𝑎
𝑏
𝑐
𝑒
𝑓
𝑎
𝑏
𝑒
𝑓
𝑎
𝑐
superscript
𝑞
1
𝑛
𝑎
𝑞
𝑞
{\displaystyle{\displaystyle{{}_{4}\phi_{3}}\left({q^{-n},a,b,c\atop d,e,f};q,%
q\right)=\frac{\left(e/a,f/a;q\right)_{n}}{\left(e,f;q\right)_{n}}a^{n}{{}_{4}%
\phi_{3}}\left({q^{-n},a,d/b,d/c\atop d,aq^{1-n}/e,aq^{1-n}/f};q,q\right)=%
\frac{\left(a,ef/(ab),ef/(ac);q\right)_{n}}{\left(e,f,ef/(abc);q\right)_{n}}{{%
}_{4}\phi_{3}}\left({q^{-n},e/a,f/a,ef/(abc)\atop ef/(ab),ef/(ac),q^{1-n}/a};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)}}
(
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}}
Identifiers
