DLMF:26.9.E5 (Q7878)

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DLMF:26.9.E5
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    test
    ∑ n = 0 ∞ p k ⁡ ( n ) ⁢ q n = ∏ j = 1 k 1 1 - q j = 1 + ∑ m = 1 ∞ [ k + m - 1 m ] q ⁢ q m , superscript subscript 𝑛 0 partition-function-at-most 𝑘 𝑛 superscript 𝑞 𝑛 superscript subscript product 𝑗 1 𝑘 1 1 superscript 𝑞 𝑗 1 superscript subscript 𝑚 1 q-binomial 𝑘 𝑚 1 𝑚 𝑞 superscript 𝑞 𝑚 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}p_{k}\left(n\right)q^{n}=\prod_% {j=1}^{k}\frac{1}{1-q^{j}}=1+\sum_{m=1}^{\infty}\genfrac{[}{]}{0.0pt}{}{k+m-1}% {m}_{q}q^{m},}}
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    DLMF id
    DLMF:26.9.E5
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