DLMF:24.19.E3 (Q7595)

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DLMF:24.19.E3
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    Statements

    Defining formula
    t 2 cosh ⁡ t - 1 = - 2 ⁢ ∑ n = 0 ∞ ( 2 ⁢ n - 1 ) ⁢ B 2 ⁢ n ⁢ t 2 ⁢ n ( 2 ⁢ n ) ! , superscript 𝑡 2 𝑡 1 2 superscript subscript 𝑛 0 2 𝑛 1 Bernoulli-number-B 2 𝑛 superscript 𝑡 2 𝑛 2 𝑛 {\displaystyle{\displaystyle\frac{t^{2}}{\cosh t-1}=-2\sum_{n=0}^{\infty}(2n-1% )B_{2n}\frac{t^{2n}}{(2n)!},}}
    0 references
    DLMF id
    DLMF:24.19.E3
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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.m1aadec
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    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
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    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2adec
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    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1bdec
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    Q12111
    Defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C24.S1.XMD6.m1dec
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