We know that for Bessel functions with same index the orthogonality condition holds: $$ \int_0^{+\infty}J_\mu(k x)J_\mu(k' x) k' x dx=\delta(k-k') $$ Is it possible to obtain an analytic result for($\mu \neq\nu$)? $$ I=\int_0^{+\infty}J_\mu(k x)J_\nu(k' x) k' x dx $$ In the similar question(Delta-function representations, Bessel function) one of the answers says that it is equal to zero which is dubious.
2026-03-29 05:49:59.1774763399
Orthogonality of Bessel functions with different indices
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