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DLMF:27.7.E5 - MaRDI portal

DLMF:27.7.E5 (Q8738)

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DLMF:27.7.E5
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    Statements

    DLMF defining formula
    ∑ n = 1 ∞ n α ⁢ x n 1 - x n = ∑ n = 1 ∞ σ α ⁡ ( n ) ⁢ x n , superscript subscript 𝑛 1 superscript 𝑛 𝛼 superscript 𝑥 𝑛 1 superscript 𝑥 𝑛 superscript subscript 𝑛 1 divisor-sigma 𝛼 𝑛 superscript 𝑥 𝑛 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}n^{\alpha}\frac{x^{n}}{1-x^{n}}% =\sum_{n=1}^{\infty}\sigma_{\alpha}\left(n\right)x^{n},}}
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    constraint
    | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}}
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    Symbols used
    sum of powers of divisors of $$n$$
    DLMF defining formula
    σ α ⁡ ( n ) divisor-sigma 𝛼 𝑛 {\displaystyle{\displaystyle\sigma_{\NVar{\alpha}}\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E10.m2adec
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    positive integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1ddec
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    real number
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1ddec
    0 references
     
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