skip to main content

Title: Symbolic methods for the evaluation of sum rules of Bessel functions

The use of the umbral formalism allows a significant simplification of the derivation of sum rules involving products of special functions and polynomials. We rederive in this way known sum rules and addition theorems for Bessel functions. Furthermore, we obtain a set of new closed form sum rules involving various special polynomials and Bessel functions. The examples we consider are relevant for applications ranging from plasma physics to quantum optics.
Authors:
 [1] ;  [2] ;  [3] ;  [4]
  1. INFN - Laboratori Nazionali di Frascati, via E. Fermi 40, IT 00044 Frascati, Roma (Italy)
  2. ENEA - Centro Ricerche Frascati, via E. Fermi 45, IT 00044 Frascati, Roma (Italy)
  3. H. Niewodniczański Institute of Nuclear Physics, Polish Academy of Sciences, ul.Eljasza-Radzikowskiego 152, PL 31342 Kraków, Poland and Instituto de Física, Universidade de São Paulo, P.O. Box 66318, B 05315-970 São Paulo, SP (Brazil)
  4. Laboratoire de Physique Théorique de la Matière Condensée, Université Pierre et Marie Curie, CNRS UMR 7600, Tour 13 - 5ième ét., B.C. 121, 4 pl. Jussieu, F 75252 Paris Cedex 05 (France)
Publication Date:
OSTI Identifier:
22218269
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 54; Journal Issue: 7; Other Information: (c) 2013 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICAL METHODS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BESSEL FUNCTIONS; OPTICS; PLASMA; POLYNOMIALS; SUM RULES