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DLMF:27.7.E6 - MaRDI portal

DLMF:27.7.E6 (Q8739)

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DLMF:27.7.E6
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    Statements

    DLMF defining formula
    ∑ n = 1 ∞ λ ⁡ ( n ) ⁢ x n 1 - x n = ∑ n = 1 ∞ x n 2 . superscript subscript 𝑛 1 Liouville-lambda 𝑛 superscript 𝑥 𝑛 1 superscript 𝑥 𝑛 superscript subscript 𝑛 1 superscript 𝑥 superscript 𝑛 2 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}\lambda\left(n\right)\frac{x^{n% }}{1-x^{n}}=\sum_{n=1}^{\infty}x^{n^{2}}.}}
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    constraint
    | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}}
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    Symbols used
    Liouville’s function
    DLMF defining formula
    λ ⁡ ( n ) Liouville-lambda 𝑛 {\displaystyle{\displaystyle\lambda\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E13.m2adec
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    positive integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1edec
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    real number
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1edec
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    Identifiers

     
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