DLMF:24.4.E32 (Q7445)

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DLMF:24.4.E32
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    Statements

    Defining formula
    B 2 ⁢ n ⁡ ( 1 6 ) = B 2 ⁢ n ⁡ ( 5 6 ) = 1 2 ⁢ ( 1 - 2 1 - 2 ⁢ n ) ⁢ ( 1 - 3 1 - 2 ⁢ n ) ⁢ B 2 ⁢ n , Bernoulli-polynomial-B 2 𝑛 1 6 Bernoulli-polynomial-B 2 𝑛 5 6 1 2 1 superscript 2 1 2 𝑛 1 superscript 3 1 2 𝑛 Bernoulli-number-B 2 𝑛 {\displaystyle{\displaystyle B_{2n}\left(\tfrac{1}{6}\right)=B_{2n}\left(% \tfrac{5}{6}\right)=\tfrac{1}{2}(1-2^{1-2n})(1-3^{1-2n})B_{2n},}}
    0 references
    DLMF id
    DLMF:24.4.E32
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1aldec
    0 references
    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.m2apdec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1aedec
    0 references
     
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