What is the solution of the integral: $\int_0^a J_s(k_1 \rho)J_{s+1} (k_2 \rho ) \rho~ d\rho $ where the integer $s \ge 0 $
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Are you sure that's supposed to be $s+1$ and not $s$ ? I think you should refer to the orthogonality of Bessel functions. – Prasun Biswas Oct 08 '17 at 21:22
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Yeah, I'd like to know know solution about difference order. Especially when the difference is 1. – Sang T. Kim Oct 09 '17 at 01:43
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In that case, I'd try using the recurrence relations for Bessel functions and then invoke orthogonality. – Prasun Biswas Oct 09 '17 at 01:45