DLMF:8.11.E16 (Q2589): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5aadec
Property / Symbols used
 
Property / Symbols used: Q11329 / rank
 
Normal rank
Property / Symbols used: Q11329 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11329 / qualifier
 
xml-id: C8.S1.XMD6.m1edec
Property / Symbols used
 
Property / Symbols used: function (locally) / rank
 
Normal rank
Property / Symbols used: function (locally) / qualifier
 
Defining formula:

S n ⁢ ( x ) subscript 𝑆 𝑛 𝑥 {\displaystyle{\displaystyle S_{n}(x)}}

S_{n}(x)
Property / Symbols used: function (locally) / qualifier
 
xml-id: C8.S11.XMD6.m1bdec

Latest revision as of 13:55, 2 January 2020

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DLMF:8.11.E16
No description defined

    Statements

    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
    DLMF id
    DLMF:8.11.E16
    0 references
    Symbols used
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11acdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2akdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    Q11329
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C8.S1.XMD6.m1edec
    0 references
    function (locally)
    Defining formula
    S n ⁢ ( x ) subscript 𝑆 𝑛 𝑥 {\displaystyle{\displaystyle S_{n}(x)}}
    xml-id
    C8.S11.XMD6.m1bdec
    0 references
     
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