DLMF:25.5.E9 (Q7622): Difference between revisions

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

ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}

\Riemannzeta@{\NVar{s}}
Property / Symbols used: Riemann zeta function / qualifier
 
xml-id: C25.S2.E1.m2ahdec

Revision as of 13:26, 2 January 2020

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DLMF:25.5.E9
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    Statements

    Defining formula
    ζ ⁡ ( s ) = 2 s - 1 Γ ⁡ ( s + 1 ) ⁢ ∫ 0 ∞ x s ( sinh ⁡ x ) 2 ⁢ d x , Riemann-zeta 𝑠 superscript 2 𝑠 1 Euler-Gamma 𝑠 1 superscript subscript 0 superscript 𝑥 𝑠 superscript 𝑥 2 𝑥 {\displaystyle{\displaystyle\zeta\left(s\right)=\frac{2^{s-1}}{\Gamma\left(s+1% \right)}\int_{0}^{\infty}\frac{x^{s}}{(\sinh x)^{2}}\mathrm{d}x,}}
    0 references
    DLMF id
    DLMF:25.5.E9
    0 references
    constraint
    ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
    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.m2agdec
    0 references
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2ahdec
    0 references
     
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