Hi. Im trying to integrate the function exp(a*cos(x)) from zero to infinit, where a is a constant. First Ive rewritten it to Bessel functions of the first kind like this:(adsbygoogle = window.adsbygoogle || []).push({});

exp(z*cos(x))=BesselI(0,z)+sum(BesselI(v,z)*cos(v*x),v=1..infinit)

where BesselI is the modified Bessel function of the first kind. The last term is the sum over v from 1 to infinit and v is an integer. Is this correct?

Secondly Im trying to get Maple to do the integral using the modified Bessel functions, but I cant get it to work. Can anybody help me? Thank you for your time.

Best regards

Anne

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# Integration of the function exp(cos(x))

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