arXiv math/04053092004-05math.CAmath.RT

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

Tom H. Koornwinder, Uri Onn

备注：: changed title, references updated, minor changes matching the version to appear in Ramanujan J.; 22 pp
发表信息：: Ramanujan J. 13 (2007), 365-387
DOI：: 10.1007/s11139-006-0258-9

英文摘要：

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.

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