DLMF:8.21.E27 (Q2749): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: auxiliary function (locally) / rank
 
Normal rank
Property / Symbols used: auxiliary function (locally) / qualifier
 
Defining formula:

g ( a , z ) 𝑔 𝑎 𝑧 {\displaystyle{\displaystyle g(a,z)}}

g(a,z)
Property / Symbols used: auxiliary function (locally) / qualifier
 
xml-id: C8.S21.XMD2.m1edec

Latest revision as of 14:20, 2 January 2020

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DLMF:8.21.E27
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    Statements

    g ( a , z ) z a - 1 k = 0 ( - 1 ) k ( 1 - a ) 2 k + 1 z 2 k + 1 . asymptotic-expansion 𝑔 𝑎 𝑧 superscript 𝑧 𝑎 1 superscript subscript 𝑘 0 superscript 1 𝑘 Pochhammer 1 𝑎 2 𝑘 1 superscript 𝑧 2 𝑘 1 {\displaystyle{\displaystyle g(a,z)\sim z^{a-1}\sum_{k=0}^{\infty}\frac{(-1)^{% k}{\left(1-a\right)_{2k+1}}}{z^{2k+1}}.}}
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    DLMF:8.21.E27
    0 references
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    C5.S2.SS3.m1acdec
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    asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    C2.S1.SS3.p1.m11aadec
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    z 𝑧 {\displaystyle{\displaystyle z}}
    C8.S1.XMD2.m1wdec
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    a 𝑎 {\displaystyle{\displaystyle a}}
    C8.S1.XMD3.m1xdec
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    k 𝑘 {\displaystyle{\displaystyle k}}
    C8.S1.XMD5.m1edec
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    g ( a , z ) 𝑔 𝑎 𝑧 {\displaystyle{\displaystyle g(a,z)}}
    C8.S21.XMD2.m1edec
    0 references