DLMF:25.11.E10 (Q7684)

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DLMF:25.11.E10
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    Statements

    Defining formula
    ζ ⁡ ( s , a ) = ∑ n = 0 ∞ ( s ) n n ! ⁢ ζ ⁡ ( n + s ) ⁢ ( 1 - a ) n , Hurwitz-zeta 𝑠 𝑎 superscript subscript 𝑛 0 Pochhammer 𝑠 𝑛 𝑛 Riemann-zeta 𝑛 𝑠 superscript 1 𝑎 𝑛 {\displaystyle{\displaystyle\zeta\left(s,a\right)=\sum_{n=0}^{\infty}\frac{{% \left(s\right)_{n}}}{n!}\zeta\left(n+s\right)(1-a)^{n},}}
    0 references
    DLMF id
    DLMF:25.11.E10
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    constraint
    | a - 1 | < 1 𝑎 1 1 {\displaystyle{\displaystyle|a-1|<1}}
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    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Hurwitz zeta function
    Defining formula
    ζ ⁡ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S11.E1.m2akdec
    0 references
    Q10759
    Defining formula
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1adec
    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
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