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DLMF:17.2.E50
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Formula:6037
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MaRDI QID
Q6037
Label: DLMF:17.2.E50
Digital Library of Mathematical Functions ID
17.2.E50
1
+
∑
n
=
1
∞
q
n
2
+
n
(
1
-
q
)
(
1
-
q
2
)
⋯
(
1
-
q
n
)
=
∏
n
=
0
∞
1
(
1
-
q
5
n
+
2
)
(
1
-
q
5
n
+
3
)
.
1
superscript
subscript
𝑛
1
superscript
𝑞
superscript
𝑛
2
𝑛
1
𝑞
1
superscript
𝑞
2
⋯
1
superscript
𝑞
𝑛
superscript
subscript
product
𝑛
0
1
1
superscript
𝑞
5
𝑛
2
1
superscript
𝑞
5
𝑛
3
{\displaystyle{\displaystyle 1+\sum_{n=1}^{\infty}\frac{q^{n^{2}+n}}{(1-q)(1-q% ^{2})\cdots(1-q^{n})}=\prod_{n=0}^{\infty}\frac{1}{(1-q^{5n+2})(1-q^{5n+3})}.}}
Constraint(s)
Symbols List
q
𝑞
{\displaystyle{\displaystyle q}}
: complex base
n
𝑛
{\displaystyle{\displaystyle n}}
: nonnegative integer
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