Asymptotic root distribution of Charlier polynomials with large
negative parameter

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

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

References:

Journal of Mathematical Analysis and Applications

Impact factor

Impact factor: 1.200

RIV identification code

RIV/47813059:19610/23:A0000125

Organization unit

Mathematical Institute in Opava

DOI

https://doi.org/10.1016/j.jmaa.2023.127086

UT WoS

000944363200001

EID Scopus

2-s2.0-85148722295

Keywords in English

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

Links

GBP201/12/G028, research and development project.

Changed: 8/4/2024 12:15, Mgr. Aleš Ryšavý

Abstract

In the original language

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.

Cite

BLASCHKE, Petr and František ŠTAMPACH. Asymptotic root distribution of Charlier polynomials with large negative parameter. Journal of Mathematical Analysis and Applications. San Diego (USA): Academic Press Inc. Elsevier Science, 2023, vol. 524, No 2, p. "127086-1"-"127086-29", 29 pp. ISSN 0022-247X. Available from: https://doi.org/10.1016/j.jmaa.2023.127086.

@article{78041,
   author = {Blaschke, Petr and Štampach, František},
   article_location = {San Diego (USA)},
   article_number = {2},
   doi = {https://doi.org/10.1016/j.jmaa.2023.127086},
   keywords = {Charlier polynomials; Asymptotic root distribution; Variable parameter; Non-standard parameter},
   language = {eng},
   issn = {0022-247X},
   journal = {Journal of Mathematical Analysis and Applications},
   title = {Asymptotic root distribution of Charlier polynomials with large negative parameter},
   url = {https://www.sciencedirect.com/science/article/pii/S0022247X23000896},
   volume = {524},
   year = {2023}
}

TY  - JOUR
ID  - 78041
AU  - Blaschke, Petr - Štampach, František
PY  - 2023
TI  - Asymptotic root distribution of Charlier polynomials with large negative parameter
JF  - Journal of Mathematical Analysis and Applications
VL  - 524
IS  - 2
SP  - "127086-1"-"127086-29"
EP  - "127086-1"-"127086-29"
PB  - Academic Press Inc. Elsevier Science
SN  - 0022247X
KW  - Charlier polynomials
KW  - Asymptotic root distribution
KW  - Variable parameter
KW  - Non-standard parameter
UR  - https://www.sciencedirect.com/science/article/pii/S0022247X23000896
N2  - 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.
ER  -

BLASCHKE, Petr and František ŠTAMPACH. Asymptotic root distribution of Charlier polynomials with large negative parameter. \textit{Journal of Mathematical Analysis and Applications}. San Diego (USA): Academic Press Inc. Elsevier Science, 2023, vol.~524, No~2, p.~''127086-1''-''127086-29'', 29 pp. ISSN~0022-247X. Available from: https://doi.org/10.1016/j.jmaa.2023.127086.

Přehled o publikaci