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arXiv · 2104.10169

An Exact Integral-to-Sum Relation for Products of Bessel Functions

Oliver H. E. Philcox·Zachary Slepian
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Abstract

A useful identity relating the infinite sum of two Bessel functions to their infinite integral was discovered in Dominici et al. (2012). Here, we extend this result to products of $N$ Bessel functions, and show it can be straightforwardly proven using the Abel-Plana theorem, or the Poisson summation formula. For $N=2$, the proof is much simpler than that of Dominici et al., and significantly enlarges the range of validity.

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Oliver H. E. Philcox, Zachary Slepian. 2021-04-20. An Exact Integral-to-Sum Relation for Products of Bessel Functions. https://doi.org/10.1098/rspa.2021.0376

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