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DLMF:27.14.E3 - MaRDI portal

DLMF:27.14.E3 (Q8795)

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DLMF:27.14.E3
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    Statements

    DLMF defining formula
    1 f ⁡ ( x ) = ∑ n = 0 ∞ p ⁡ ( n ) ⁢ x n , 1 Euler-phi 𝑥 superscript subscript 𝑛 0 partition-function 𝑛 superscript 𝑥 𝑛 {\displaystyle{\displaystyle\frac{1}{\mathit{f}\left(x\right)}=\sum_{n=0}^{% \infty}p\left(n\right)x^{n},}}
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    constraint
    | x | < 1 𝑥 1 {\displaystyle{\displaystyle|x|<1}}
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    Symbols used
    Euler’s reciprocal function
    DLMF defining formula
    f ⁡ ( x ) Euler-phi 𝑥 {\displaystyle{\displaystyle\mathit{f}\left(\NVar{x}\right)}}
    xml-id
    C27.S14.E2.m2aadec
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    total number of partitions of n
    DLMF defining formula
    p ⁡ ( n ) partition-function 𝑛 {\displaystyle{\displaystyle p\left(\NVar{n}\right)}}
    xml-id
    C26.S2.Px4.p2.m5adec
    0 references
    positive integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1adec
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    real number
    DLMF defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C27.S1.XMD6.m1adec
    0 references
     
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