Some open problems of generalised Bessel polynomials

Abstract

The solution of several open problems connected with the generalised Bessel polynomials, which appear in solving the wave equation in spherical coordinates and in network synthesis and design, is shown. In particular, explicit and simple recursion formulae for sums of powers and product sums of the zeros of these polynomials are found. Also, three different sets of sums of generalised Bessel polynomials are analytically evaluated in a compact way.