A completeness-like relation for Bessel functions

2013/10/03 by Paulo Henrique Flose Reimberg, Reimberg, Paulo H. F., L. Raul Abramo +1
Mathematics · #46B15 #60J60 #60K35 #82C41 #Advanced Mathematical Identities #FOS: Physical sciences #Functional Equations Stability Results #Mathematical Physics (math-ph) #Mathematical functions and polynomials #Statistical Mechanics (cond-mat.stat-mech)

paper · pdf · doi:10.48550/arxiv.1310.1128

openalex publication_date 2013/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 L²[0, 1].

Related

• A partial converse to the Riemann--Lebesgue lemma for Bessel--Fourier series of order zero
• A recursive algorithm for an efficient and accurate computation of incomplete Bessel functions
• Cohomology and Bessel functions Theory
• Integral representation for Bessel's functions of the first kind and\n Neumann series
• On a generalization of the Bessel function Neumann expansion