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A completeness-like relation for Bessel functions

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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 $L^2[0, 1]$.
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Dates and versions

cea-01333489 , version 1 (17-06-2016)

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Paulo H. F. Reimberg, L. Raul Abramo. A completeness-like relation for Bessel functions. 2016. ⟨cea-01333489⟩
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