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DLMF:26.10.E2 - MaRDI portal
Statements
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restricted-partitions-P
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{\displaystyle{\displaystyle\sum_{n=0}^{\infty}p\left(\mathcal{D},n\right)q^{n%
}=\prod_{j=1}^{\infty}(1+q^{j})=\prod_{j=1}^{\infty}\frac{1}{1-q^{2j-1}}=1+%
\sum_{m=1}^{\infty}\frac{q^{m(m+1)/2}}{(1-q)(1-q^{2})\cdots(1-q^{m})}=1+\sum_{%
m=1}^{\infty}q^{m}(1+q)(1+q^{2})\cdots\*(1+q^{m-1}),}}
p
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condition
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n
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restricted-partitions-P
condition
𝑛
{\displaystyle{\displaystyle p\left(\NVar{\mathrm{condition}},\NVar{n}\right)}}
j
𝑗
{\displaystyle{\displaystyle j}}
m
𝑚
{\displaystyle{\displaystyle m}}
n
𝑛
{\displaystyle{\displaystyle n}}
q
𝑞
{\displaystyle{\displaystyle q}}
Identifiers