DLMF:27.14.E6 (Q8105)

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DLMF:27.14.E6
No description defined

    Statements

    Defining formula
    p ⁡ ( n ) = ∑ k = 1 ∞ ( - 1 ) k + 1 ⁢ ( p ⁡ ( n - ω ⁢ ( k ) ) + p ⁡ ( n - ω ⁢ ( - k ) ) ) = p ⁡ ( n - 1 ) + p ⁡ ( n - 2 ) - p ⁡ ( n - 5 ) - p ⁡ ( n - 7 ) + ⋯ , partition-function 𝑛 superscript subscript 𝑘 1 superscript 1 𝑘 1 partition-function 𝑛 𝜔 𝑘 partition-function 𝑛 𝜔 𝑘 partition-function 𝑛 1 partition-function 𝑛 2 partition-function 𝑛 5 partition-function 𝑛 7 ⋯ {\displaystyle{\displaystyle p\left(n\right)=\sum_{k=1}^{\infty}(-1)^{k+1}% \left(p\left(n-\omega(k)\right)+p\left(n-\omega(-k)\right)\right)=p\left(n-1% \right)+p\left(n-2\right)-p\left(n-5\right)-p\left(n-7\right)+\cdots,}}
    0 references
    DLMF id
    DLMF:27.14.E6
    0 references
    Symbols used
    Q12187
    Defining formula
    p ⁡ ( n ) partition-function 𝑛 {\displaystyle{\displaystyle p\left(\NVar{n}\right)}}
    xml-id
    C26.S2.Px4.p2.m5aadec
    0 references
    Q12238
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C27.S1.XMD2.m1bdec
    0 references
    Q12234
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1bdec
    0 references
    pentagonal numbers (locally)
    Defining formula
    ω ⁢ ( k ) 𝜔 𝑘 {\displaystyle{\displaystyle\omega(k)}}
    xml-id
    C27.S14.XMD1.m1bdec
    0 references
     
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