J 2020

The asymptotic zero distribution of Lommel polynomials as functions of their order with a variable complex argument

BLASCHKE, Petr and František ŠTAMPACH

Basic information

Original name

The asymptotic zero distribution of Lommel polynomials as functions of their order with a variable complex argument

Authors

BLASCHKE, Petr (203 Czech Republic, 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, 2020, 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

RIV identification code

RIV/47813059:19610/20:A0000065

Organization unit

Mathematical Institute in Opava

UT WoS

000535982700031

Keywords in English

Lommel polynomials; Zeros; Asymptotic zero distribution; Variable parameters

Tags

Tags

International impact, Reviewed

Links

GBP201/12/G028, research and development project.
Změněno: 17/3/2021 12:48, Mgr. Aleš Ryšavý

Abstract

V originále

We study the asymptotic distribution of roots of Lommel polynomials as polynomials of the order with a variable and purely imaginary argument. The roots are complex and accumulate on certain curves in the complex plane. We prove existence of the weak limit of corresponding root-counting measures and deduce formulas for the supporting curves and density. The obtained result represents a solvable example of a more general problem which is still open. Numerical illustrations of the main result are also involved.