Hi g_edgar,
Thank you for your reply. I tried with Maple too and I got this:
a*hypergeom([1/2, 1/2], [1, 1, 3/2], -a^2*b^2)
The equation you got must be the result of this integral: \int _{0}^{a}\! {{\rm J}_0\left(bx\right)}{dx}
I have to search for the generalized...