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DLMF:8.11.E16 - MaRDI portal

DLMF:8.11.E16 (Q3287)

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DLMF:8.11.E16
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    Statements

    DLMF defining formula
    S n ⁢ ( 1 ) - 1 2 ⁢ n ! ⁢ e n n n ∼ - 2 3 + 4 135 ⁢ n - 1 - 8 2835 ⁢ n - 2 - 16 8505 ⁢ n - 3 + … , asymptotic-expansion subscript 𝑆 𝑛 1 1 2 𝑛 superscript 𝑒 𝑛 superscript 𝑛 𝑛 2 3 4 135 superscript 𝑛 1 8 2835 superscript 𝑛 2 16 8505 superscript 𝑛 3 … {\displaystyle{\displaystyle S_{n}(1)-\frac{1}{2}\frac{n!e^{n}}{n^{n}}\sim-% \tfrac{2}{3}+\tfrac{4}{135}n^{-1}-\tfrac{8}{2835}n^{-2}-\tfrac{16}{8505}n^{-3}% +\dots,}}
    0 references
    Symbols used
    Q10905
    DLMF defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11acdec
    0 references
    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2akdec
    0 references
    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C8.S1.XMD6.m1edec
    0 references
    function (locally)
    DLMF defining formula
    S n ⁢ ( x ) subscript 𝑆 𝑛 𝑥 {\displaystyle{\displaystyle S_{n}(x)}}
    xml-id
    C8.S11.XMD6.m1bdec
    0 references

    Identifiers

     
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