Definite Integral of exp*BesselK ?
- From: Paul Menzel <sobloher@xxxxxxxx>
- Date: Wed, 02 Apr 2008 09:54:03 EDT
Hi everybody,
does anyone have an idea how to solve the integral
\int_0^a exp(-b*x) K_0(x) dx
analytically, where K_0(x) is the modified Besselfunction of the second kind and a and b are real and >0 ?
I didn't find anything like this in Abramovitz, Prudnikov or Co. nor any method in there, that could be helpful (the reduction formula for Indefinite integrals didn't help much here as b is in principle arbitrary.)
In my desperation, I already thought of expanding the exponential into a Taylor-Series as the integral
\int_0^a x^n K_0(x) dx
with n being an integer can in principle be solved for any n using the recurrence relations for repeated integrals of K_0 - but I didn't get a closed representation for any n from that...
Any ideas or hints?
Many thanks and cheers, Paul
.
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