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Statements
𝒟
q
n
ϕ
1
2
(
a
,
b
c
;
q
,
z
d
)
=
(
a
,
b
;
q
)
n
d
n
(
c
;
q
)
n
(
1
-
q
)
n
ϕ
1
2
(
a
q
n
,
b
q
n
c
q
n
;
q
,
d
z
)
,
superscript
subscript
𝒟
𝑞
𝑛
q-hypergeometric-rphis
2
1
𝑎
𝑏
𝑐
𝑞
𝑧
𝑑
q-multiple-Pochhammer
𝑎
𝑏
𝑞
𝑛
superscript
𝑑
𝑛
q-Pochhammer-symbol
𝑐
𝑞
𝑛
superscript
1
𝑞
𝑛
q-hypergeometric-rphis
2
1
𝑎
superscript
𝑞
𝑛
𝑏
superscript
𝑞
𝑛
𝑐
superscript
𝑞
𝑛
𝑞
𝑑
𝑧
{\displaystyle{\displaystyle\mathcal{D}_{q}^{n}{{}_{2}\phi_{1}}\left({a,b\atop
c%
};q,zd\right)=\frac{\left(a,b;q\right)_{n}d^{n}}{\left(c;q\right)_{n}(1-q)^{n}%
}{{}_{2}\phi_{1}}\left({aq^{n},bq^{n}\atop cq^{n}};q,dz\right),}}
(
a
;
q
)
n
q-Pochhammer-symbol
𝑎
𝑞
𝑛
{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
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}}
z
𝑧
{\displaystyle{\displaystyle z}}
𝒟
q
subscript
𝒟
𝑞
{\displaystyle{\displaystyle\mathcal{D}_{q}}}
Identifiers
