Asymptotic root distribution of Charlier polynomials with large negative parameter

@article{78041,
   author = {Blaschke, Petr and Štampach, František},
   article_location = {San Diego (USA)},
   article_number = {2},
   doi = {http://dx.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 a 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, roč.~524, č.~2, s.~''127086-1''-''127086-29'', 29 s. ISSN~0022-247X. Dostupné z: https://dx.doi.org/10.1016/j.jmaa.2023.127086.