DLMF:26.8.E41 (Q7869)

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DLMF:26.8.E41
No description defined

    Statements

    Defining formula
    s ⁡ ( n + k , k ) ∼ ( - 1 ) n 2 n ⁢ n ! ⁢ k 2 ⁢ n , asymptotically-equals Stirling-number-first-kind-S 𝑛 𝑘 𝑘 superscript 1 𝑛 superscript 2 𝑛 𝑛 superscript 𝑘 2 𝑛 {\displaystyle{\displaystyle s\left(n+k,k\right)\sim\frac{(-1)^{n}}{2^{n}n!}k^% {2n},}}
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    DLMF id
    DLMF:26.8.E41
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    constraint
    k → ∞ → 𝑘 {\displaystyle{\displaystyle k\to\infty}}
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    Symbols used
    Q12132
    Defining formula
    s ⁡ ( n , k ) Stirling-number-first-kind-S 𝑛 𝑘 {\displaystyle{\displaystyle s\left(\NVar{n},\NVar{k}\right)}}
    xml-id
    C26.S8.SS1.p1.m5avdec
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    asymptotic equality
    Defining formula
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2aadec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5andec
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    Q12174
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C26.S1.XMD4.m1ahdec
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    Q12172
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C26.S1.XMD6.m1amdec
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