DLMF:25.6.E3 (Q7640)

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DLMF:25.6.E3
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    Statements

    Defining formula
    ζ ⁡ ( - n ) = - B n + 1 n + 1 , Riemann-zeta 𝑛 Bernoulli-number-B 𝑛 1 𝑛 1 {\displaystyle{\displaystyle\zeta\left(-n\right)=-\frac{B_{n+1}}{n+1},}}
    0 references
    DLMF id
    DLMF:25.6.E3
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    constraint
    n = 1 , 2 , 3 , … 𝑛 1 2 3 … {\displaystyle{\displaystyle n=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.m1aadec
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    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2abdec
    0 references
    Q12148
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1adec
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