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 and František ŠTAMPACH
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.