DLMF:25.11.E8 (Q7682)

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DLMF:25.11.E8
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    Statements

    Defining formula
    ζ ⁡ ( s , 1 2 ⁢ a ) = ζ ⁡ ( s , 1 2 ⁢ a + 1 2 ) + 2 s ⁢ ∑ n = 0 ∞ ( - 1 ) n ( n + a ) s , Hurwitz-zeta 𝑠 1 2 𝑎 Hurwitz-zeta 𝑠 1 2 𝑎 1 2 superscript 2 𝑠 superscript subscript 𝑛 0 superscript 1 𝑛 superscript 𝑛 𝑎 𝑠 {\displaystyle{\displaystyle\zeta\left(s,\tfrac{1}{2}a\right)=\zeta\left(s,% \tfrac{1}{2}a+\tfrac{1}{2}\right)+2^{s}\sum_{n=0}^{\infty}\frac{(-1)^{n}}{(n+a% )^{s}},}}
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    DLMF id
    DLMF:25.11.E8
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    constraint
    ℜ ⁡ s > 0 𝑠 0 {\displaystyle{\displaystyle\Re s>0}}
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    s ≠ 1 𝑠 1 {\displaystyle{\displaystyle s\neq 1}}
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    0 < a ≤ 1 0 𝑎 1 {\displaystyle{\displaystyle 0<a\leq 1}}
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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.m2aidec
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