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A completeness-like relation for Bessel functions

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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Preprints, Working Papers, ...
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Submitted on : Friday, June 17, 2016 - 3:40:48 PM
Last modification on : Monday, December 13, 2021 - 9:16:04 AM
Long-term archiving on: : Sunday, September 18, 2016 - 11:09:43 AM


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  • HAL Id : cea-01333489, version 1
  • ARXIV : 1310.1128


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



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