Some families of generating functions for the Jacobi and related orthogonal polynomials

By making use of the familiar group-theoretic (Lie algebraic) method of Louis Weisner (1899-1988), many authors recently proved various single- and multiple-series generating functions for the so-called extended Jacobi polynomials. The main object of the present sequel to these earlier works is to show how easily each of such generating functions can be derived from the corresponding known result for the classical Jacobi polynomials. Many general families of bilinear, bilateral, or mixed multilateral generating functions for the Jacobi and related orthogonal polynomials, which are seemingly relevant to the present investigation, are also considered here. (C) 1999 Academic Press.