Bessel type orthogonal polynomials

Abstract

The Bessel type polynomials considered are orthogonal with respect to the weight function obtained from the Bessel weight function on R by adding a scalar multiple of the Dirac delta function at 0. Since Bessel type orthogonal polynomial sequence (OPS) is semi-classical, its weight function ω satisfies (σ(x)ω)``-τ(x)ω=g(x) where σ(x), τ(x) are some polynomials and g(x) have 0-moments. We can get the real weight function of Bessel type OPS by solving non-homogeneous weight equation.