Comparative asymptotics for discrete semiclassical orthogonal polynomials

被引：1

作者：

Dominici, Diego ^{[1
]}

机构：

[1] Johannes Kepler Univ Linz, Res Inst Symbol Computat, Altenberger Str 69, A-4040 Linz, Austria

来源：

BULLETIN OF MATHEMATICAL SCIENCES | 2023年 / 13卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

Semiclassical orthogonal polynomials; asymptotic expansions; ordinary differential equations; RELATIVE ASYMPTOTICS; RECURRENCE COEFFICIENTS; RESPECT; CHARLIER; LATTICES; SERIES;

D O I：

10.1142/S1664360722500102

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the ratio P-n(x;z)/phi(n)(x) asymptotically as n -> infinity, where the polynomials P-n(x; z) are orthogonal with respect to a discrete linear functional and phi(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 <=( )2. We show several plots illustrating the accuracy of our results.

引用

页数：36

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