On a method for the construction of some q-orthogonal polynomials

Abstract

This paper fully relies on the results of our paper [12] where we considered the orthogonality of rational functions W n (s) as the Laplace transform images of a set of orthoexponential functions, obtained from Jacobi polynomials, and as the Laplace transform images of Laguerre polynomials. In Ref. [12] we proved that the orthogonality of Jacobi and Laguerre polynomials is induced by the orthogonality of the functions W n (s). In Section 1 of this paper we have given all the necessary information for one to more easily follow the Section 2 where we have derived q-analogues of the Legendre, Chebyshev and Laguerre polynomials by means of the inverse q-Laplace transform of rational functions W q,n (s) which correspond to rational functions W n (s).