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

Big q-Jacobi polynomials {P(n)(.; a, b, c; q)}(n=0)(infinity) are classically defined for 0 < a < q(-1), 0 < b < q(-1) and c < 0. For the family of little q-Jacobi polynomials {p(n)(.; a, b vertical bar q)}(n=0)(infinity), 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.