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

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‎Changed an Item: Add constraint
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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

    Defining formula
    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}}.}}
    0 references
    DLMF id
    DLMF:8.21.E27
    0 references
    Symbols used
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1acdec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11aadec
    0 references
    Q11323
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C8.S1.XMD2.m1wdec
    0 references
    Q11324
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C8.S1.XMD3.m1xdec
    0 references
    Q11330
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C8.S1.XMD5.m1edec
    0 references
    auxiliary function (locally)
    Defining formula
    g ⁢ ( a , z ) 𝑔 𝑎 𝑧 {\displaystyle{\displaystyle g(a,z)}}
    xml-id
    C8.S21.XMD2.m1edec
    0 references
     
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