DLMF:25.16.E10 (Q7766)

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DLMF:25.16.E10
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    Statements

    Defining formula
    H ⁡ ( - 2 ⁢ a ) = 1 2 ⁢ ζ ⁡ ( 1 - 2 ⁢ a ) = - B 2 ⁢ a 4 ⁢ a , Euler-sum-H 2 𝑎 1 2 Riemann-zeta 1 2 𝑎 Bernoulli-number-B 2 𝑎 4 𝑎 {\displaystyle{\displaystyle H\left(-2a\right)=\frac{1}{2}\zeta\left(1-2a% \right)=-\frac{B_{2a}}{4a},}}
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    DLMF id
    DLMF:25.16.E10
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    constraint
    a = 1 , 2 , 3 , … 𝑎 1 2 3 … {\displaystyle{\displaystyle a=1,2,3,\dots}}
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    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1adec
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    Q12169
    Defining formula
    H ⁡ ( s ) Euler-sum-H 𝑠 {\displaystyle{\displaystyle H\left(\NVar{s}\right)}}
    xml-id
    C25.S16.SS2.p1.m1aedec
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