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Question: Problems integrating Bessel functions

Question:Problems integrating Bessel functions

chrisc 111 Maple 2021
integration besselj
March 29 2021
2

Hi folks

I'm trying to integrate products of Bessel functions and reproduce known results in the literature. For example, the integral

Int(BesselJ(0,k*r)*BesselJ(1,q*r),r=0..infinity);

should evaluate to 1/q if q>k and 0 if q<k, but maple only gives the first solution, even when 'assuming q<k' is specified. It should give 1/2q when k=q -- which it does but only when I put k=q in the integral. For some reason, it always assumes q>k whatever I do. 

There's a lot of examples like this. Am I missing something? Is there a way to return an answer with all the (correct!) solutions?

Thanks in advance.
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