DLMF:13.9.E9 (Q4452): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
Defining formula:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2adec

Revision as of 16:00, 2 January 2020

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DLMF:13.9.E9
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    Statements

    Defining formula
    z = ± ( 2 ⁢ n + a ) ⁢ π ⁢ i + ln ⁡ ( - Γ ⁡ ( a ) Γ ⁡ ( b - a ) ⁢ ( ± 2 ⁢ n ⁢ π ⁢ i ) b - 2 ⁢ a ) + O ⁡ ( n - 1 ⁢ ln ⁡ n ) , 𝑧 plus-or-minus 2 𝑛 𝑎 𝜋 imaginary-unit Euler-Gamma 𝑎 Euler-Gamma 𝑏 𝑎 superscript plus-or-minus 2 𝑛 𝜋 imaginary-unit 𝑏 2 𝑎 Big-O superscript 𝑛 1 𝑛 {\displaystyle{\displaystyle z=\pm(2n+a)\pi\mathrm{i}+\ln\left(-\frac{\Gamma% \left(a\right)}{\Gamma\left(b-a\right)}\left(\pm 2n\pi\mathrm{i}\right)^{b-2a}% \right)+O\left(n^{-1}\ln n\right),}}
    0 references
    DLMF id
    DLMF:13.9.E9
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aadec
    0 references
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2adec
    0 references
     
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