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I'm trying to compute the following integral (in LaTeX notation; * denotes multiplication)

\int_0^{2\pi} exp (k_1 * cos (t + k_2)) d t

with k_1 and k_2 being known constants. Furthermore k_2 is between 0 and 2 pi.

From Wikipedia [1] I get the following formula

\int_0^{2\pi} exp (k * cos (t)) d t = 2\pi I_0 (k)

where I_0 is a Bessel function of the first kind. I must admit I can't figure if I can change my original problem into one that is solvable using the equation from Wikipedia. If not, does anybody have any ideas on how to solve this?

Thanks

Søren

[1] http://en.wikipedia.org/wiki/List_of_integrals_of_exponential_functions

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# Integrating exp(k1*cos (t + k2)) from 0 to 2*pi

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