DLMF:2.10.E4 (Q991)

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DLMF:2.10.E4
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    Statements

    Defining formula
    S ⁢ ( n ) = 1 2 ⁢ n 2 ⁢ ln ⁡ n - 1 4 ⁢ n 2 + 1 2 ⁢ n ⁢ ln ⁡ n + 1 12 ⁢ ln ⁡ n + C + ∑ s = 2 m - 1 ( - B 2 ⁢ s ) 2 ⁢ s ⁢ ( 2 ⁢ s - 1 ) ⁢ ( 2 ⁢ s - 2 ) ⁢ 1 n 2 ⁢ s - 2 + R m ⁢ ( n ) , 𝑆 𝑛 1 2 superscript 𝑛 2 𝑛 1 4 superscript 𝑛 2 1 2 𝑛 𝑛 1 12 𝑛 𝐶 superscript subscript 𝑠 2 𝑚 1 Bernoulli-number-B 2 𝑠 2 𝑠 2 𝑠 1 2 𝑠 2 1 superscript 𝑛 2 𝑠 2 subscript 𝑅 𝑚 𝑛 {\displaystyle{\displaystyle S(n)=\tfrac{1}{2}n^{2}\ln n-\tfrac{1}{4}n^{2}+% \tfrac{1}{2}n\ln n+\tfrac{1}{12}\ln n+C+\sum_{s=2}^{m-1}\frac{(-B_{2s})}{2s(2s% -1)(2s-2)}\frac{1}{n^{2s-2}}+R_{m}(n),}}
    0 references
    DLMF id
    DLMF:2.10.E4
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1abdec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2aadec
    0 references
    Q11112
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C2.S10.XMD2.m1bdec
    0 references
    Q11113
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C2.S10.XMD3.m1cdec
    0 references
    Q11115
    Defining formula
    S ⁢ ( n ) 𝑆 𝑛 {\displaystyle{\displaystyle S(n)}}
    xml-id
    C2.S10.XMD5.m1adec
    0 references
    Q11116
    Defining formula
    C 𝐶 {\displaystyle{\displaystyle C}}
    xml-id
    C2.S10.XMD6.m1dec
    0 references
    Q11117
    Defining formula
    R m ⁢ ( n ) subscript 𝑅 𝑚 𝑛 {\displaystyle{\displaystyle R_{m}(n)}}
    xml-id
    C2.S10.XMD7.m1dec
    0 references
     
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