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

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

2004-05-15

arxiv.org/abs/math/0405309v4

Ramanujan J. 13 (2007), 365-387

Mathematics

Classical Analysis and ODEs

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

Scientific paper

10.1007/s11139-006-0258-9

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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