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Statements
∑
n
=
0
∞
q
n
2
(
q
2
;
q
2
)
n
(
q
;
q
2
)
n
=
coeff. of
z
0
in
(
-
z
q
;
q
2
)
∞
(
-
z
-
1
q
;
q
2
)
∞
(
q
2
;
q
2
)
∞
(
-
z
-
1
;
q
2
)
∞
(
q
;
q
2
)
∞
(
z
-
1
;
q
2
)
∞
=
1
(
q
;
q
2
)
∞
coeff. of
z
0
in
(
-
z
q
;
q
2
)
∞
(
-
z
-
1
q
;
q
2
)
∞
(
q
2
;
q
2
)
∞
(
z
-
2
;
q
4
)
∞
=
G
(
q
4
)
(
q
;
q
2
)
∞
,
superscript
subscript
𝑛
0
superscript
𝑞
superscript
𝑛
2
q-Pochhammer-symbol
superscript
𝑞
2
superscript
𝑞
2
𝑛
q-Pochhammer-symbol
𝑞
superscript
𝑞
2
𝑛
coeff. of
superscript
𝑧
0
in
q-Pochhammer-symbol
𝑧
𝑞
superscript
𝑞
2
q-Pochhammer-symbol
superscript
𝑧
1
𝑞
superscript
𝑞
2
q-Pochhammer-symbol
superscript
𝑞
2
superscript
𝑞
2
q-Pochhammer-symbol
superscript
𝑧
1
superscript
𝑞
2
q-Pochhammer-symbol
𝑞
superscript
𝑞
2
q-Pochhammer-symbol
superscript
𝑧
1
superscript
𝑞
2
1
q-Pochhammer-symbol
𝑞
superscript
𝑞
2
coeff. of
superscript
𝑧
0
in
q-Pochhammer-symbol
𝑧
𝑞
superscript
𝑞
2
q-Pochhammer-symbol
superscript
𝑧
1
𝑞
superscript
𝑞
2
q-Pochhammer-symbol
superscript
𝑞
2
superscript
𝑞
2
q-Pochhammer-symbol
superscript
𝑧
2
superscript
𝑞
4
𝐺
superscript
𝑞
4
q-Pochhammer-symbol
𝑞
superscript
𝑞
2
{\displaystyle{\displaystyle\sum_{n=0}^{\infty}\frac{q^{n^{2}}}{\left(q^{2};q^%
{2}\right)_{n}\left(q;q^{2}\right)_{n}}=\mbox{ coeff. of }z^{0}\mbox{ in }%
\frac{\left(-zq;q^{2}\right)_{\infty}\left(-z^{-1}q;q^{2}\right)_{\infty}\left%
(q^{2};q^{2}\right)_{\infty}}{\left(-z^{-1};q^{2}\right)_{\infty}\left(q;q^{2}%
\right)_{\infty}\left(z^{-1};q^{2}\right)_{\infty}}=\frac{1}{\left(q;q^{2}%
\right)_{\infty}}\mbox{ coeff. of }z^{0}\mbox{ in }\frac{\left(-zq;q^{2}\right%
)_{\infty}\left(-z^{-1}q;q^{2}\right)_{\infty}\left(q^{2};q^{2}\right)_{\infty%
}}{\left(z^{-2};q^{4}\right)_{\infty}}=\frac{G(q^{4})}{\left(q;q^{2}\right)_{%
\infty}},}}
(
a
;
q
)
n
q-Pochhammer-symbol
𝑎
𝑞
𝑛
{\displaystyle{\displaystyle\left(\NVar{a};\NVar{q}\right)_{\NVar{n}}}}
q
𝑞
{\displaystyle{\displaystyle q}}
n
𝑛
{\displaystyle{\displaystyle n}}
z
𝑧
{\displaystyle{\displaystyle z}}
G
(
q
)
𝐺
𝑞
{\displaystyle{\displaystyle G(q)}}
Identifiers
