About some identities for Bessel polynomials

摘要

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