About some identities for Bessel polynomials

TL;DR

This paper derives new identities involving Bessel polynomials using a probabilistic approach based on properties of the Generalized Inverse Gaussian distribution, expanding on recent work with Bessel function identities.

Contribution

It introduces novel identities for Bessel polynomials by applying probabilistic methods, offering an alternative to generating function techniques.

Findings

New identities for Bessel polynomials derived

Probabilistic approach provides alternative derivation

Connections to Generalized Inverse Gaussian distribution established

Abstract

In a recent paper, Yu. A. Brychkov derived a series of identities for multiples sums of special functions, using generating functions. Among these identities, a particularly interesting one involves multiples sums of Bessel $I_{\nu}$ functions with half-integer indices. We derive here some equivalent identities that involve different kinds of Bessel polynomials, sing a probabilistic approach based on the properties of the Generalized Inverse Gaussian probability density.