DLMF:25.5.E21 (Q7634): 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.m2akdec

Revision as of 13:29, 2 January 2020

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DLMF:25.5.E21
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    Statements

    Defining formula
    ζ ⁡ ( s ) = Γ ⁡ ( 1 - s ) 2 ⁢ π ⁢ i ⁢ ( 1 - 2 1 - s ) ⁢ ∫ - ∞ ( 0 + ) z s - 1 e - z + 1 ⁢ d z , Riemann-zeta 𝑠 Euler-Gamma 1 𝑠 2 𝜋 𝑖 1 superscript 2 1 𝑠 superscript subscript limit-from 0 superscript 𝑧 𝑠 1 superscript 𝑒 𝑧 1 𝑧 {\displaystyle{\displaystyle\zeta\left(s\right)=\frac{\Gamma\left(1-s\right)}{% 2\pi i(1-2^{1-s})}\*\int_{-\infty}^{(0+)}\frac{z^{s-1}}{e^{-z}+1}\mathrm{d}z,}}
    0 references
    DLMF id
    DLMF:25.5.E21
    0 references
    constraint
    s ≠ 1 , 2 , … 𝑠 1 2 … {\displaystyle{\displaystyle s\neq 1,2,\dots}}
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2akdec
    0 references
     
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