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Statements
S
n
(
x
;
q
)
=
∑
ℓ
=
0
n
q
ℓ
2
(
-
x
)
ℓ
(
q
;
q
)
ℓ
(
q
;
q
)
n
-
ℓ
=
1
(
q
;
q
)
n
ϕ
1
1
(
q
-
n
0
;
q
,
-
q
n
+
1
x
)
.
Stieltjes-Wigert-polynomial-S
𝑛
𝑥
𝑞
superscript
subscript
ℓ
0
𝑛
superscript
𝑞
superscript
ℓ
2
superscript
𝑥
ℓ
q-Pochhammer-symbol
𝑞
𝑞
ℓ
q-Pochhammer-symbol
𝑞
𝑞
𝑛
ℓ
1
q-Pochhammer-symbol
𝑞
𝑞
𝑛
q-hypergeometric-rphis
1
1
superscript
𝑞
𝑛
0
𝑞
superscript
𝑞
𝑛
1
𝑥
{\displaystyle{\displaystyle S_{n}\left(x;q\right)=\sum_{\ell=0}^{n}\frac{q^{%
\ell^{2}}(-x)^{\ell}}{\left(q;q\right)_{\ell}\left(q;q\right)_{n-\ell}}=\frac{%
1}{\left(q;q\right)_{n}}{{}_{1}\phi_{1}}\left({q^{-n}\atop 0};q,-q^{n+1}x%
\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)}}
q
𝑞
{\displaystyle{\displaystyle q}}
ℓ
ℓ
{\displaystyle{\displaystyle\ell}}
n
𝑛
{\displaystyle{\displaystyle n}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
