On the limit relations between classical continuous and discrete orthogonal polynomials

Abstract

Limit relations between classical continuous (Jacobi, Laguerre, Hermite) and discrete (Charlier, Meixner, Kravchuk, Hahn) orthogonal polynomials are well known and can be described by relations of type lim λ → ∞ P n ( x; λ) = Q n ( x). Deeper information on these limiting processes can be obtained from the expansion P n(x;λ) = ∑ k=0 ∞ R k(x;n) λ k . In this paper a method for the recursive computation of coefficients R k ( x; n) is designed being the main tool the consideration of a closely related connection problem which can be solved, also recurrently, by using an algorithm recently developed by the authors.