About some identities for Bessel polynomials

Abstract

In the paper [1], Yu. A. Brychkov derived a set of identities for multiple sums of special functions, using generating functions. Among these identities, a particularly interesting one involves multiple sums of Bessel Iν functions with half-integer indices. We derive here some equivalent identities that involve different kinds of Bessel polynomials, using a probabilistic approach based on the properties of the Generalized Inverse Gaussian probability density