DLMF:4.36.E4 (Q1918)

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DLMF:4.36.E4
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    Statements

    Defining formula
    csch 2 ⁡ z = ∑ n = - ∞ ∞ 1 ( z - n ⁢ π ⁢ i ) 2 , 2 𝑧 superscript subscript 𝑛 1 superscript 𝑧 𝑛 𝜋 𝑖 2 {\displaystyle{\displaystyle{\operatorname{csch}^{2}}z=\sum_{n=-\infty}^{% \infty}\frac{1}{(z-n\pi i)^{2}},}}
    0 references
    DLMF id
    DLMF:4.36.E4
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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.m2acdec
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    hyperbolic cosecant function
    Defining formula
    csch ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{csch}\NVar{z}}}
    xml-id
    C4.S28.E5.m2adec
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    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q11223
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C4.S1.XMD3.m1cdec
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