Connection relations and bilinear formulas for the classical orthogonal polynomials

Abstract

Suppose we have an operator T that maps a set of orthogonal polynomials { P n ( x )} n = o ∞ to another set of orthogonal polynomials. We show how such a mapping can be used to derive connection relations as well as bilinear formulas for the pre-images { P n ( x )} n = o ∞ . This method is carried out in detail for the Jacobi, Laguerre, and Hahn polynomials.