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. © 2013 AIP Publishing LLC.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics
Babusci, D., Dattoli, G., Górska, K., & Penson, K. A. (2013). Symbolic methods for the evaluation of sum rules of Bessel functions. Journal of Mathematical Physics, 54(7), -. . https://doi.org/10.1063/1.4812325