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DLMF:4.36.E3 - MaRDI portal

DLMF:4.36.E3 (Q2315)

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DLMF:4.36.E3
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    Statements

    DLMF defining formula
    coth ⁡ z = 1 z + 2 ⁢ z ⁢ ∑ n = 1 ∞ 1 z 2 + n 2 ⁢ π 2 , hyperbolic-cotangent 𝑧 1 𝑧 2 𝑧 superscript subscript 𝑛 1 1 superscript 𝑧 2 superscript 𝑛 2 superscript 𝜋 2 {\displaystyle{\displaystyle\coth z=\frac{1}{z}+2z\sum_{n=1}^{\infty}\frac{1}{% z^{2}+n^{2}\pi^{2}},}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    DLMF defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    hyperbolic cotangent function
    DLMF defining formula
    coth ⁡ z hyperbolic-cotangent 𝑧 {\displaystyle{\displaystyle\coth\NVar{z}}}
    xml-id
    C4.S28.E7.m2adec
    0 references
    integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C4.S1.XMD3.m1bdec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C4.S1.XMD8.m1bdec
    0 references

    Identifiers

     
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