2020
The asymptotic zero distribution of Lommel polynomials as functions of their order with a variable complex argument
BLASCHKE, Petr and František ŠTAMPACHBasic 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
Article in a journal
Field of Study
10101 Pure mathematics
Country of publisher
United States of America
Confidentiality degree
is not subject to a state or trade secret
Impact factor
Impact factor: 1.583
RIV identification code
RIV/47813059:19610/20:A0000065
Organization unit
Mathematical Institute in Opava
UT WoS
000535982700031
EID Scopus
2-s2.0-85084829226
Keywords in English
Lommel polynomials; Zeros; Asymptotic zero distribution; Variable parameters
Tags
Tags
International impact, Reviewed
Links
GBP201/12/G028, research and development project.
Changed: 17/3/2021 12:48, Mgr. Aleš Ryšavý
Abstract
In the original language
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.