I would like to evaluate the following integral $\int\limits_{0}^{\infty} \dfrac{\cos \left(\omega t\right)}{\cosh ^{\sigma}\left(t\right)} dt$ where $\sigma$ and $\omega$ are positive real constants. If you have noticed this integral in any table or handbook, lease let me know. Thanks for your help...
Integral Involving Cos and Cosh
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definite-integrals
hyperbolic-functions
trigonometric-integrals
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1If $\sigma\in\mathbb{N}$, such integral is pretty simple to compute through the residue theorem. Otherwise, hypergeometric functions are involved. – 2017-02-12
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0Any luck to have closed form solution in terms of $\sigma$ for $\omega = 0$? – 2017-02-15
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0The same applies also if $\omega=0$. There are simple closed-form solutions for $\sigma\in\mathbb{N}$ but for a general $\sigma$ the value of the integral is given by a hypergeometric function. – 2017-02-15