DLMF:4.40.E9 (Q1981)

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DLMF:4.40.E9
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    Statements

    test
    ∫ - ∞ ∞ e a ⁢ x ( cosh ⁡ ( 1 2 ⁢ x ) ) 2 ⁢ d x = 4 ⁢ π ⁢ a sin ⁡ ( π ⁢ a ) , superscript subscript superscript 𝑒 𝑎 𝑥 superscript 1 2 𝑥 2 𝑥 4 𝜋 𝑎 𝜋 𝑎 {\displaystyle{\displaystyle\int_{-\infty}^{\infty}\frac{e^{ax}}{\left(\cosh% \left(\tfrac{1}{2}x\right)\right)^{2}}\mathrm{d}x=\frac{4\pi a}{\sin\left(\pi a% \right)},}}
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    DLMF id
    DLMF:4.40.E9
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    constraint
    - 1 < a < 1 1 𝑎 1 {\displaystyle{\displaystyle-1<a<1}}
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