[Submitted on 20 Apr 2021] (cross-list from math.CA)
An Exact Integral-to-Sum Relation for Products of Bessel Functions
Oliver H. E. Philcox🇺🇸 · Zachary Slepian🇺🇸
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.
- Comments:
- 15 pages, 1 figure. Submitted to Proc. Roy. Soc. A
- Subjects:
- math.CA (math.CA); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics — Theory (hep-th); Mathematical Physics (math-ph); math.MP (math.MP); Nuclear Theory (nucl-th)
- arXiv:
- 2104.10169 [pdf]