An Exact Integral-to-Sum Relation for Products of Bessel Functions
Classical Analysis and ODEs
2021-11-17 v2 Cosmology and Nongalactic Astrophysics
High Energy Physics - Theory
Mathematical Physics
math.MP
Nuclear Theory
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 Bessel functions, and show it can be straightforwardly proven using the Abel-Plana theorem, or the Poisson summation formula. For , the proof is much simpler than that of Dominici et al., and significantly enlarges the range of validity.
Keywords
Cite
@article{arxiv.2104.10169,
title = {An Exact Integral-to-Sum Relation for Products of Bessel Functions},
author = {Oliver H. E. Philcox and Zachary Slepian},
journal= {arXiv preprint arXiv:2104.10169},
year = {2021}
}
Comments
15 pages, 1 figure. Submitted to Proc. Roy. Soc. A