DLMF:2.10.E5 (Q992)

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DLMF:2.10.E5
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    Statements

    Defining formula
    R m ⁢ ( n ) = ∫ n ∞ B ~ 2 ⁢ m ⁡ ( x ) - B 2 ⁢ m 2 ⁢ m ⁢ ( 2 ⁢ m - 1 ) ⁢ x 2 ⁢ m - 1 ⁢ d x . subscript 𝑅 𝑚 𝑛 superscript subscript 𝑛 periodic-Bernoulli-polynomial-B 2 𝑚 𝑥 Bernoulli-number-B 2 𝑚 2 𝑚 2 𝑚 1 superscript 𝑥 2 𝑚 1 𝑥 {\displaystyle{\displaystyle R_{m}(n)=\int_{n}^{\infty}\frac{\widetilde{B}_{2m% }\left(x\right)-B_{2m}}{2m(2m-1)x^{2m-1}}\mathrm{d}x.}}
    0 references
    DLMF id
    DLMF:2.10.E5
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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.m1acdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1abdec
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    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3abdec
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    Q11110
    Defining formula
    B ~ n ⁡ ( x ) periodic-Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle\widetilde{B}_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS3.m1aadec
    0 references
    Q11112
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C2.S10.XMD2.m1cdec
    0 references
    Q11113
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S10.XMD3.m1ddec
    0 references
     
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