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Statements
ϕ
n
(
z
)
=
∑
ℓ
=
0
n
(
a
q
2
;
q
2
)
ℓ
(
a
;
q
2
)
n
-
ℓ
(
q
2
;
q
2
)
ℓ
(
q
2
;
q
2
)
n
-
ℓ
(
q
-
1
z
)
ℓ
=
(
a
;
q
2
)
n
(
q
2
;
q
2
)
n
ϕ
1
2
(
a
q
2
,
q
-
2
n
a
-
1
q
2
-
2
n
;
q
2
,
q
z
a
)
,
subscript
italic-ϕ
𝑛
𝑧
superscript
subscript
ℓ
0
𝑛
q-Pochhammer-symbol
𝑎
superscript
𝑞
2
superscript
𝑞
2
ℓ
q-Pochhammer-symbol
𝑎
superscript
𝑞
2
𝑛
ℓ
q-Pochhammer-symbol
superscript
𝑞
2
superscript
𝑞
2
ℓ
q-Pochhammer-symbol
superscript
𝑞
2
superscript
𝑞
2
𝑛
ℓ
superscript
superscript
𝑞
1
𝑧
ℓ
q-Pochhammer-symbol
𝑎
superscript
𝑞
2
𝑛
q-Pochhammer-symbol
superscript
𝑞
2
superscript
𝑞
2
𝑛
q-hypergeometric-rphis
2
1
𝑎
superscript
𝑞
2
superscript
𝑞
2
𝑛
superscript
𝑎
1
superscript
𝑞
2
2
𝑛
superscript
𝑞
2
𝑞
𝑧
𝑎
{\displaystyle{\displaystyle\phi_{n}(z)=\sum_{\ell=0}^{n}\frac{\left(aq^{2};q^%
{2}\right)_{\ell}\left(a;q^{2}\right)_{n-\ell}}{\left(q^{2};q^{2}\right)_{\ell%
}\left(q^{2};q^{2}\right)_{n-\ell}}(q^{-1}z)^{\ell}=\frac{\left(a;q^{2}\right)%
_{n}}{\left(q^{2};q^{2}\right)_{n}}{{}_{2}\phi_{1}}\left({aq^{2},q^{-2n}\atop a%
^{-1}q^{2-2n}};q^{2},\frac{qz}{a}\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)}}
z
𝑧
{\displaystyle{\displaystyle z}}
q
𝑞
{\displaystyle{\displaystyle q}}
ℓ
ℓ
{\displaystyle{\displaystyle\ell}}
n
𝑛
{\displaystyle{\displaystyle n}}
ϕ
n
(
z
)
subscript
italic-ϕ
𝑛
𝑧
{\displaystyle{\displaystyle\phi_{n}(z)}}
Identifiers
