离散半经典正交多项式的比较渐近性

IF 1.1 2区数学 Q1 MATHEMATICS

Bulletin of Mathematical Sciences Pub Date : 2022-10-28 DOI:10.1142/s1664360722500102

D. Dominici

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引用次数: 1

摘要

我们研究了比值pn (x;z) φ n (x)渐近为n→∞，其中多项式pn (x;Z)相对于离散线性泛函是正交的，φ n (x)表示下降阶乘多项式。我们给出了允许计算np (x)的高阶渐近展开式的递归式。Z)，并给出了s≤2类的大多数离散半经典多项式的例子。我们展示了几个图来说明我们的结果的准确性。

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Comparative asymptotics for discrete semiclassical orthogonal polynomials

We study the ratio P n ( x ; z ) φ n ( x ) asymptotically as n → ∞ , 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 ≤ 2 . We show several plots illustrating the accuracy of our results.

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来源期刊

Bulletin of Mathematical Sciences MATHEMATICS-

CiteScore

2.10

自引率

0.00%

发文量

审稿时长

13 weeks

期刊介绍： The Bulletin of Mathematical Sciences, a peer-reviewed, open access journal, will publish original research work of highest quality and of broad interest in all branches of mathematical sciences. The Bulletin will publish well-written expository articles (40-50 pages) of exceptional value giving the latest state of the art on a specific topic, and short articles (up to 15 pages) containing significant results of wider interest. Most of the expository articles will be invited. The Bulletin of Mathematical Sciences is launched by King Abdulaziz University, Jeddah, Saudi Arabia.