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Comparative asymptotics for discrete semiclassical orthogonal polynomials

Research Institute for Symbolic Computation, Johannes Kepler University Linz, Altenberger Straße 69, 4040 Linz, Austria

https://doi.org/10.1142/S1664360722500102Cited by:0 (Source: Crossref)

Abstract

We study the ratio $\frac{P_{n} (x; z)}{ϕ_{n} (x)}$ asymptotically as $n \to \infty$ , where the polynomials $P_{n} (x; z)$ are orthogonal with respect to a discrete linear functional and $ϕ_{n} (x)$ denote the falling factorial polynomials. We give recurrences that allow the computation of high order asymptotic expansions of $P_{n} (x; z)$ and give examples for most discrete semiclassical polynomials of class $s \leq 2$ . We show several plots illustrating the accuracy of our results.

Communicated by Ari Laptev

Keywords:

AMSC: 41A60, 33C47, 34E05

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Vol. 13, No. 01

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History

Received 31 January 2022

Revised 28 September 2022

Accepted 22 October 2022

Published: 26 November 2022

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This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Comparative asymptotics for discrete semiclassical orthogonal polynomials

Abstract

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