LU factorizations, q=0 limits, and p-adic interpretations of some q-hypergeometric orthogonal polynomials

Abstract

For little q-Jacobi polynomials and q-Hahn polynomials we give particular q-hypergeometric series representations in which the termwise q=0 limit can be taken. When rewritten in matrix form, these series representations can be viewed as LU factorizations. We develop a general theory of LU factorizations related to complete systems of orthogonal polynomials with discrete orthogonality relations which admit a dual system of orthogonal polynomials. For the q=0 orthogonal limit functions we discuss interpretations on p-adic spaces. In the little 0-Jacobi case we also discuss product formulas.