DLMF:4.40.E8 (Q1980)

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DLMF:4.40.E8
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    Statements

    Defining formula
    ∫ 0 ∞ sinh ⁡ ( a ⁢ x ) sinh ⁡ ( π ⁢ x ) ⁢ d x = 1 2 ⁢ tan ⁡ ( 1 2 ⁢ a ) , superscript subscript 0 𝑎 𝑥 𝜋 𝑥 𝑥 1 2 1 2 𝑎 {\displaystyle{\displaystyle\int_{0}^{\infty}\frac{\sinh\left(ax\right)}{\sinh% \left(\pi x\right)}\mathrm{d}x=\tfrac{1}{2}\tan\left(\tfrac{1}{2}a\right),}}
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    DLMF id
    DLMF:4.40.E8
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    constraint
    - π < a < π 𝜋 𝑎 𝜋 {\displaystyle{\displaystyle-\pi<a<\pi}}
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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.m2aadec
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    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1agdec
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    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2addec
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