(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The integral is

[tex]\int _{-\pi }^{\pi }\!{\frac {{{\rm e}^{x\cos \left( \theta \right) }} \cos \left( n\theta \right) }{\pi }}{d\theta}.[/tex]

3. The attempt at a solution

I've tried a couple of alternative methods huddling in my mind to solve this integral, but none of them worked. Actually using De Moivre's formula and integrationa by parts this can be written as

[tex]{\frac {{{\rm e}^{x+in\pi }}-{{\rm e}^{-x-in\pi }}}{\pi }}+\int _{-\pi }^{\pi }\!{\frac {x\sin \left( \theta \right) {{\rm e}^{x\cos\left( \theta \right) +in\theta}}}{in\pi }}{d\theta}.[/tex]

where we hit the second integral which, in its indefinite form, cannot be described by the elementary functions.

Any help will be appreciated!

AB

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# Homework Help: A serious Fourier integral

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