DLMF:4.22.E5 (Q1752)

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DLMF:4.22.E5
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    Statements

    Defining formula
    csc ⁡ z = 1 z + 2 ⁢ z ⁢ ∑ n = 1 ∞ ( - 1 ) n z 2 - n 2 ⁢ π 2 . 𝑧 1 𝑧 2 𝑧 superscript subscript 𝑛 1 superscript 1 𝑛 superscript 𝑧 2 superscript 𝑛 2 superscript 𝜋 2 {\displaystyle{\displaystyle\csc z=\frac{1}{z}+2z\sum_{n=1}^{\infty}\frac{(-1)% ^{n}}{z^{2}-n^{2}\pi^{2}}.}}
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    DLMF id
    DLMF:4.22.E5
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
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