DLMF:4.36.E5 (Q1919)

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DLMF:4.36.E5
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    Statements

    Defining formula
    csch ⁡ 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\operatorname{csch}z=\frac{1}{z}+2z\sum_{n=1}^{% \infty}\frac{(-1)^{n}}{z^{2}+n^{2}\pi^{2}}.}}
    0 references
    DLMF id
    DLMF:4.36.E5
    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.m2addec
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    hyperbolic cosecant function
    Defining formula
    csch ⁡ z 𝑧 {\displaystyle{\displaystyle\operatorname{csch}\NVar{z}}}
    xml-id
    C4.S28.E5.m2aadec
    0 references
    Q11223
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C4.S1.XMD3.m1ddec
    0 references
    Q11217
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1ddec
    0 references
     
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