Delta-function representations, Bessel function

Solution 1:

In general, $\mu$ and $\nu$ are not equal, representation in the form of series can be obtained if you replace the product of only Bessel function under the integral by expansion in series where each term is expressed via hypergeometric function $_2F_1$ (see Bateman and Erdelyi, Higher Transcedental Functions, Volume $2$, Chapter $7 (7.2.7$). Then you can integrate term by term.

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