DLMF:24.16.E10 (Q7580)

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DLMF:24.16.E10
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    Statements

    Defining formula
    ∑ a = 1 f χ ⁢ ( a ) ⁢ t ⁢ e a ⁢ t e f ⁢ t - 1 = ∑ n = 0 ∞ B n , χ ⁢ t n n ! , superscript subscript 𝑎 1 𝑓 𝜒 𝑎 𝑡 superscript 𝑒 𝑎 𝑡 superscript 𝑒 𝑓 𝑡 1 superscript subscript 𝑛 0 subscript 𝐵 𝑛 𝜒 superscript 𝑡 𝑛 𝑛 {\displaystyle{\displaystyle\sum_{a=1}^{f}\frac{\chi(a)te^{at}}{e^{ft}-1}=\sum% _{n=0}^{\infty}B_{n,\chi}\frac{t^{n}}{n!},}}
    0 references
    DLMF id
    DLMF:24.16.E10
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2acdec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5agdec
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    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1idec
    0 references
    Q12111
    Defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C24.S1.XMD6.m1fdec
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    Q12138
    Defining formula
    χ ⁢ ( a ) 𝜒 𝑎 {\displaystyle{\displaystyle\chi(a)}}
    xml-id
    C24.S16.XMD3.m1dec
    0 references
    Q12139
    Defining formula
    f 𝑓 {\displaystyle{\displaystyle f}}
    xml-id
    C24.S16.XMD4.m1dec
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    Q12140
    Defining formula
    B n , χ subscript 𝐵 𝑛 𝜒 {\displaystyle{\displaystyle B_{n,\chi}}}
    xml-id
    C24.S16.XMD5.m1dec
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