DLMF:25.8.E2 (Q7659)

From DRMF
Revision as of 13:33, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:25.8.E2
No description defined

    Statements

    Defining formula
    ∑ k = 0 ∞ Γ ⁡ ( s + k ) ( k + 1 ) ! ⁢ ( ζ ⁡ ( s + k ) - 1 ) = Γ ⁡ ( s - 1 ) , superscript subscript 𝑘 0 Euler-Gamma 𝑠 𝑘 𝑘 1 Riemann-zeta 𝑠 𝑘 1 Euler-Gamma 𝑠 1 {\displaystyle{\displaystyle\sum_{k=0}^{\infty}\frac{\Gamma\left(s+k\right)}{(% k+1)!}\left(\zeta\left(s+k\right)-1\right)=\Gamma\left(s-1\right),}}
    0 references
    DLMF id
    DLMF:25.8.E2
    0 references
    constraint
    s ≠ 1 , 0 , - 1 , - 2 , … 𝑠 1 0 1 2 … {\displaystyle{\displaystyle s\neq 1,0,-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.m2adec
    0 references
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7659&oldid=37557"