Non-classical orthogonality relations for big and little q-Jacobi polynomials

Big q-Jacobi polynomials {Pn(·; a, b, c; q)}∞n=0 are classically defined for 0 < a < q −1, 0 < b < q−1 and c < 0. For the family of little q-Jacobi polynomials {pn(·; a, b|q)}∞n=0, classical considerations restrict the parameters imposing 0 < a < q−1 and b < q−1. In this work we extend both families in such a way that wider sets of parameters are allowed, and we establish orthogonality conditions for those cases for which Favard’s theorem does not work. As a by-product, we obtain similar results for the families of big and little q-Laguerre polynomials. c © 2009 Elsevier Inc. All rights reserved.