Can this integral be solved analytically?

[madness]

Hi everyone.

I have an integral I would like to solve. So far I've just been solving it numerically, but I wondered if it might be possible to get an analytical result.

Here it is:

$$\int_{-\infty}^{\infty} e^{k\cos(\omega t-a)}e^{-(bt-c)^2/(2\sigma^2)} dt$$

 

[UltrafastPED]

Try Wolfram Alpha - it will tell you!

 

[madness]

Thanks for the tip, but I'm just getting "standard computation time exceeded" on the website version :). I wonder if there's any point looking at contour integrals and the residue theorem?

 

[UltrafastPED]

I would try Wolfram Alpha as an indefinite integral ... that should get a quick answer!

I think that would be worth a try - otherwise try one of the standard texts on integration techniques:
Boros' "Irresistible Integrals: Symbolics, Analysis and Experiments in the Evaluation of Integrals"
Zwillinger's "The Handbook of Integration"

Or that old standby, "Table of Integrals, Series and Products" by Gradshteyn and Ryzhik!

Else it is back to numerical integration.