Symbolic methods for the evaluation of sum rules of Bessel functions

Author(s)

Babusci, D. ^[1] ; Dattoli, G. ^[2] ; Gorska, K. ^{[3, 4]} ; Penson, K. A. ^[5]

Affiliation

^[1] Ist Nazl Fis Nucl, Lab Nazl Frascati, IT-00044 Rome - Italy

^[2] ENEA, Ctr Ric Frascati, IT-00044 Rome - Italy

^[3] Polish Acad Sci, H Niewodniczanski Inst Nucl Phys, PL-31342 Krakow - Poland

^[4] Univ Sao Paulo, Inst Fis, BR-0531597 Sao Paulo - Brazil

^[5] Univ Paris 06, CNRS, UMR 7600, Lab Phys Theor Matiere Condensee, F-75252 Paris 05 - France

• Document type: Journal article
• Source: Journal of Mathematical Physics; v. 54, n. 7 JUL 2013.
• Web of Science Citations: 6

Abstract

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. (C) 2013 AIP Publishing LLC. (AU)

• FAPESP's process: 10/15698-5 - Coherent states and semiclassical description of quantum dissipative systems, spinning systems, and quantum relativistic particles.
• Grantee: Katarzyna Górska
• Support Opportunities: Scholarships in Brazil - Post-Doctoral