DLMF:24.4.E29 (Q7442)

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DLMF:24.4.E29
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    Statements

    Defining formula
    B 2 ⁢ n ⁡ ( 1 3 ) = B 2 ⁢ n ⁡ ( 2 3 ) = - 1 2 ⁢ ( 1 - 3 1 - 2 ⁢ n ) ⁢ B 2 ⁢ n . Bernoulli-polynomial-B 2 𝑛 1 3 Bernoulli-polynomial-B 2 𝑛 2 3 1 2 1 superscript 3 1 2 𝑛 Bernoulli-number-B 2 𝑛 {\displaystyle{\displaystyle B_{2n}\left(\tfrac{1}{3}\right)=B_{2n}\left(% \tfrac{2}{3}\right)=-\tfrac{1}{2}(1-3^{1-2n})B_{2n}.}}
    0 references
    DLMF id
    DLMF:24.4.E29
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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.m1aidec
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    Q11288
    Defining formula
    B n ⁡ ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS1.m2andec
    0 references
     
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