DLMF:5.11.E18 (Q2144)

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DLMF:5.11.E18
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    Statements

    Defining formula
    H k ⁢ ( a , b ) = ( a - b 2 ⁢ k ) ⁢ B 2 ⁢ k ( a - b + 1 ) ⁡ ( a - b + 1 2 ) . subscript 𝐻 𝑘 𝑎 𝑏 binomial 𝑎 𝑏 2 𝑘 generalized-Bernoulli-polynomial-B 𝑎 𝑏 1 2 𝑘 𝑎 𝑏 1 2 {\displaystyle{\displaystyle H_{k}(a,b)=\genfrac{(}{)}{0.0pt}{}{a-b}{2k}B^{(a-% b+1)}_{2k}\left(\frac{a-b+1}{2}\right).}}
    0 references
    DLMF id
    DLMF:5.11.E18
    0 references
    Symbols used
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1acdec
    0 references
    Q11289
    Defining formula
    B n ( ℓ ) ⁡ ( x ) generalized-Bernoulli-polynomial-B ℓ 𝑛 𝑥 {\displaystyle{\displaystyle B^{(\NVar{\ell})}_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S16.Px1.p1.m3aadec
    0 references
    Q11279
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C5.S1.XMD4.m1jdec
    0 references
    Q11275
    Defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C5.S1.XMD8.m1fdec
    0 references
    Q11283
    Defining formula
    b 𝑏 {\displaystyle{\displaystyle b}}
    xml-id
    C5.S1.XMD9.m1gdec
    0 references
     
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