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://dx.doi.org/10.1016/j.jmaa.2023.127086. |
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@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 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://dx.doi.org/10.1016/j.jmaa.2023.127086.
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