DLMF:25.11.E4 (Q7678)

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DLMF:25.11.E4
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    Statements

    Defining formula
    ζ ⁡ ( s , a ) = ζ ⁡ ( s , a + m ) + ∑ n = 0 m - 1 1 ( n + a ) s , Hurwitz-zeta 𝑠 𝑎 Hurwitz-zeta 𝑠 𝑎 𝑚 superscript subscript 𝑛 0 𝑚 1 1 superscript 𝑛 𝑎 𝑠 {\displaystyle{\displaystyle\zeta\left(s,a\right)=\zeta\left(s,a+m\right)+\sum% _{n=0}^{m-1}\frac{1}{(n+a)^{s}},}}
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    DLMF id
    DLMF:25.11.E4
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    constraint
    m = 1 , 2 , 3 , … 𝑚 1 2 3 … {\displaystyle{\displaystyle m=1,2,3,\dots}}
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    Symbols used
    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.m2acdec
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    Q12151
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C25.S1.XMD2.m1dec
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    Q12148
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1bdec
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    Q12161
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C25.S1.XMD6.m1bdec
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    Q12149
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C25.S1.XMD7.m1cdec
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