I seek a way to integrate J0, bessel function. I try to use some of the identities I can find, but it takes me no were. Please help!
The simple integral of an integer order Bessel function is given by Struve functions. You can find them in ch. 11 , "Integrals of Bessel Functions" of Abramowitz and Stegun. If you are serious about math, buy a copy (the Dover edition is inexpensive). For now you can browse an old online copy here http://www.convertit.com/Go/Convertit/Reference/AMS55.ASP