A completeness-like relation for Bessel functions
Mathematical Physics
2015-11-17 v2 Statistical Mechanics
math.MP
Abstract
Completeness relations are associated through Mercer's theorem to complete orthonormal basis of square integrable functions, and prescribe how a Dirac delta function can be decomposed into basis of eigenfunctions of a Sturm-Liouville problem. We use Gegenbauer's addition theorem to prove a relation very close to a completeness relation, but for a set of Bessel functions not known to form a complete basis in .
Keywords
Cite
@article{arxiv.1310.1128,
title = {A completeness-like relation for Bessel functions},
author = {Paulo H. F. Reimberg and L. Raul Abramo},
journal= {arXiv preprint arXiv:1310.1128},
year = {2015}
}