English

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

Classical Analysis and ODEs 2009-10-31 v4 Representation Theory

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.

Keywords

Cite

@article{arxiv.math/0405309,
  title  = {LU factorizations, q=0 limits, and p-adic interpretations of some q-hypergeometric orthogonal polynomials},
  author = {Tom H. Koornwinder and Uri Onn},
  journal= {arXiv preprint arXiv:math/0405309},
  year   = {2009}
}

Comments

changed title, references updated, minor changes matching the version to appear in Ramanujan J.; 22 pp

R2 v1 2026-07-22T17:05:33.125Z