J 2023

Asymptotic root distribution of Charlier polynomials with large negative parameter

BLASCHKE, Petr and František ŠTAMPACH

Basic information

Original name

Asymptotic root distribution of Charlier polynomials with large negative parameter

Authors

BLASCHKE, Petr (203 Czech Republic, guarantor, belonging to the institution) and František ŠTAMPACH (203 Czech Republic)

Edition

Journal of Mathematical Analysis and Applications, San Diego (USA), Academic Press Inc. Elsevier Science, 2023, 0022-247X

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Journal of Mathematical Analysis and Applications

RIV identification code

RIV/47813059:19610/23:A0000125

Organization unit

Mathematical Institute in Opava

DOI

http://dx.doi.org/10.1016/j.jmaa.2023.127086

UT WoS

000944363200001

Keywords in English

Charlier polynomials; Asymptotic root distribution; Variable parameter; Non-standard parameter

Tags

Tags

International impact, Reviewed

Links

GBP201/12/G028, research and development project.
Změněno: 8/4/2024 12:15, Mgr. Aleš Ryšavý

Abstract

V originále

We analyze the asymptotic distribution of roots of Charlier polynomials with negative parameter depending linearly on the index. The roots cluster on curves in the complex plane. We determine implicit equations for these curves and deduce the limiting density of the root distribution supported on these curves. The proof is based on a determination of the limiting Cauchy transform in a specific region and a careful application of the saddle point method. The obtained result represents a solvable example of a more general open problem.
Displayed: 24/12/2024 03:56