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DLMF:27.7.E4 - MaRDI portal

DLMF:27.7.E4 (Q8737)

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DLMF:27.7.E4
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    Statements

    DLMF defining formula
    ∑ n = 1 ∞ ϕ ⁡ ( n ) ⁢ x n 1 - x n = x ( 1 - x ) 2 , superscript subscript 𝑛 1 Euler-totient-phi 𝑛 superscript 𝑥 𝑛 1 superscript 𝑥 𝑛 𝑥 superscript 1 𝑥 2 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}\phi\left(n\right)\frac{x^{n}}{% 1-x^{n}}=\frac{x}{(1-x)^{2}},}}
    0 references
    constraint
    | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}}
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    Symbols used
    Euler’s totient
    DLMF defining formula
    ϕ ⁡ ( n ) Euler-totient-phi 𝑛 {\displaystyle{\displaystyle\phi\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E7.m2adec
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    positive integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1cdec
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    real number
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1cdec
    0 references

    Identifiers

     
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