Classical discrete orthogonal polynomials, Lah numbers, and involutory matrices

Abstract

This letter proposes two different approaches in order to solve the connection problems P n(−ξ)= ∑ m=0 n C m(n)P m(ξ), when the family { P n ( x)} belongs to a wide class of polynomials, including classical discrete orthogonal polynomials. The first approach uses the involutory character of the Lah numbers and of other specific connection coefficients. The second approach presents the recursive Navima algorithm as applied to these problems.