# Integral involving Bessel Function

• June 23rd 2009, 03:50 AM
nonsingular
Integral involving Bessel Function
Hi I have a question regarding this integral. I was wondering if someone here can help. Thanks.

Question: Evaluate $\int_0^\infty\frac{xJ_0(x)}{\sqrt{a^2+x^2}}dx$
• June 26th 2009, 10:33 AM
shawsend
Quote:

Originally Posted by nonsingular
Hi I have a question regarding this integral. I was wondering if someone here can help. Thanks.

Question: Evaluate $\int_0^\infty\frac{xJ_0(x)}{\sqrt{a^2+x^2}}dx$

The solution to this and the other one is one of the most beautiful integrations I have ever seen and wish it not go unnoticed over here:

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