DLMF:25.2.E12 (Q7607): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Euler’s constant / rank
 
Normal rank
Property / Symbols used: Euler’s constant / qualifier
 
Defining formula:

γ {\displaystyle{\displaystyle\gamma}}

\EulerConstant
Property / Symbols used: Euler’s constant / qualifier
 
xml-id: C5.S2.E3.m2adec

Revision as of 13:23, 2 January 2020

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DLMF:25.2.E12
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    Statements

    Defining formula
    ζ ⁡ ( s ) = ( 2 ⁢ π ) s ⁢ e - s - ( γ ⁢ s / 2 ) 2 ⁢ ( s - 1 ) ⁢ Γ ⁡ ( 1 2 ⁢ s + 1 ) ⁢ ∏ ρ ( 1 - s ρ ) ⁢ e s / ρ , Riemann-zeta 𝑠 superscript 2 𝜋 𝑠 superscript 𝑒 𝑠 𝑠 2 2 𝑠 1 Euler-Gamma 1 2 𝑠 1 subscript product 𝜌 1 𝑠 𝜌 superscript 𝑒 𝑠 𝜌 {\displaystyle{\displaystyle\zeta\left(s\right)=\frac{(2\pi)^{s}e^{-s-(\gamma s% /2)}}{2(s-1)\Gamma\left(\tfrac{1}{2}s+1\right)}\prod_{\rho}\left(1-\frac{s}{% \rho}\right)e^{s/\rho},}}
    0 references
    DLMF id
    DLMF:25.2.E12
    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.m2adec
    0 references
    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
    0 references
     
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