DLMF:4.19.E5 (Q1684)

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DLMF:4.19.E5
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    Statements

    Defining formula
    sec ⁡ z = 1 + z 2 2 + 5 24 ⁢ z 4 + 61 720 ⁢ z 6 + ⋯ + ( - 1 ) n ⁢ E 2 ⁢ n ( 2 ⁢ n ) ! ⁢ z 2 ⁢ n + ⋯ , 𝑧 1 superscript 𝑧 2 2 5 24 superscript 𝑧 4 61 720 superscript 𝑧 6 ⋯ superscript 1 𝑛 Euler-number-E 2 𝑛 2 𝑛 superscript 𝑧 2 𝑛 ⋯ {\displaystyle{\displaystyle\sec z=1+\frac{z^{2}}{2}+\frac{5}{24}z^{4}+\frac{6% 1}{720}z^{6}+\cdots+\frac{(-1)^{n}E_{2n}}{(2n)!}z^{2n}+\cdots,}}
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    DLMF id
    DLMF:4.19.E5
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    constraint
    | z | < 1 2 ⁢ π 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|z|<\frac{1}{2}\pi}}
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    Symbols used
    Q11238
    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
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
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