DLMF:24.2.E6 (Q8097)

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DLMF:24.2.E6
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    Statements

    DLMF defining formula
    2 ⁢ e t e 2 ⁢ t + 1 = ∑ n = 0 ∞ E n ⁢ t n n ! , 2 superscript 𝑒 𝑡 superscript 𝑒 2 𝑡 1 superscript subscript 𝑛 0 Euler-number-E 𝑛 superscript 𝑡 𝑛 𝑛 {\displaystyle{\displaystyle\frac{2e^{t}}{e^{2t}+1}=\sum_{n=0}^{\infty}E_{n}% \frac{t^{n}}{n!},}}
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    constraint
    | t | < 1 2 ⁢ π 𝑡 1 2 𝜋 {\displaystyle{\displaystyle|t|<\tfrac{1}{2}\pi}}
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    Symbols used
    Q11209
    DLMF defining formula
    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    xml-id
    C24.S2.SS2.m1adec
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    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
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    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
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    integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1edec
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    real or complex
    DLMF defining formula
    t 𝑡 {\displaystyle{\displaystyle t}}
    xml-id
    C24.S1.XMD6.m1bdec
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