A new determinant form of Bessel polynomials and applications

The Bessel polynomials are the unique polynomial solutions, with constant equal to 1, of the differential equation xy ′′ (x) + (2x+ 2)y ′ (x) − n(n+ 1)y(x) = 0 (1) They are important in certain problems of mathematical physic, for example they arise in the study of electrical networks and when the wave equation is considered on spherical coordinates. Many application may be found in [7]. In recent years new interests are arisen in determinant form of Bessel polynomials [9-11]. In this paper we purpose a new determinant form with related recurrence relation. Some application are considered, too. The Bessel polynomials are given in [1] in the form