DLMF:4.22.E4 (Q1751)

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DLMF:4.22.E4
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    Statements

    Defining formula
    csc 2 ⁡ z = ∑ n = - ∞ ∞ 1 ( z - n ⁢ π ) 2 , 2 𝑧 superscript subscript 𝑛 1 superscript 𝑧 𝑛 𝜋 2 {\displaystyle{\displaystyle{\csc^{2}}z=\sum_{n=-\infty}^{\infty}\frac{1}{(z-n% \pi)^{2}},}}
    0 references
    DLMF id
    DLMF:4.22.E4
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    cosecant function
    Defining formula
    csc ⁡ z 𝑧 {\displaystyle{\displaystyle\csc\NVar{z}}}
    xml-id
    C4.S14.E5.m2adec
    0 references
    Q11223
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C4.S1.XMD3.m1cdec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1cdec
    0 references
     
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