DLMF:25.5.E19 (Q7632): Difference between revisions

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m = 1 , 2 , 3 , 𝑚 1 2 3 {\displaystyle{\displaystyle m=1,2,3,\dots}}

m=1,2,3,\dots
Property / constraint: m = 1 , 2 , 3 , 𝑚 1 2 3 {\displaystyle{\displaystyle m=1,2,3,\dots}} / rank
 
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Revision as of 18:14, 30 December 2019

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DLMF:25.5.E19
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    ζ ( m + s ) = ( - 1 ) m - 1 Γ ( s ) sin ( π s ) π Γ ( m + s ) 0 ψ ( m ) ( 1 + x ) x - s d x , Riemann-zeta 𝑚 𝑠 superscript 1 𝑚 1 Euler-Gamma 𝑠 𝜋 𝑠 𝜋 Euler-Gamma 𝑚 𝑠 superscript subscript 0 digamma 𝑚 1 𝑥 superscript 𝑥 𝑠 𝑥 {\displaystyle{\displaystyle\zeta\left(m+s\right)=(-1)^{m-1}\frac{\Gamma\left(% s\right)\sin\left(\pi s\right)}{\pi\Gamma\left(m+s\right)}\*\int_{0}^{\infty}{% \psi^{(m)}}\left(1+x\right)x^{-s}\mathrm{d}x,}}
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    DLMF:25.5.E19
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    m = 1 , 2 , 3 , 𝑚 1 2 3 {\displaystyle{\displaystyle m=1,2,3,\dots}}
    0 references