Symbolic methods for the evaluation of sum rules of Bessel functions

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.

J. Math. Phys. vol. 54, 073501 (2013), 6 pages

References in corpus (4)

• The Ramanujan master theorem and its implications for special functions
• Hierarchical Dobinski-type relations via substitution and the moment problem
• A new class of sum rules for products of Bessel functions
• Symbolic calculus and integrals of Laguerre polynomials

Cited by in corpus (6)

• Umbral Calculus, a Different Mathematical Language
• Operational Methods in the Study of Sobolev-Jacobi Polynomials
• Operational versus umbral methods and the Borel transform
• Operational vs. Umbral Methods and Borel Transform
• Generating Functions for Lacunary Legendre and Legendre-like Polynomials
• Products of Bessel functions and associated polynomials