Open this publication in new window or tab >>2022 (English)In: Constructive approximation, ISSN 0176-4276, E-ISSN 1432-0940, Vol. 56, no 2, p. 479-Article in journal (Refereed) Published
Abstract [en]
It has been known for over 70 years that there is an asymptotic transition of Charlier polynomials to Hermite polynomials. This transition, which is still presented in its classical form in modern reference works, is valid if and only if a certain parameter is integer. In this light, it is surprising that a much more powerful transition exists from Charlier polynomials to the Hermite function, valid for any real value of the parameter. This greatly strengthens the asymptotic connections between Charlier polynomials and special functions, with applications in queueing theory, where this transition is crucial for solving first-passage problems with moving boundaries. It is shown in this paper that the convergence is locally uniform, and a sharp rate bound is proved. In addition, it is shown that there is a transition of derivatives of Charlier polynomials to the derivative of the Hermite function, again with a sharp rate bound. Finally, it is proved that zeros of Charlier polynomials converge to zeros of the Hermite function. © 2021, The Author(s).
Place, publisher, year, edition, pages
Springer, 2022
Keywords
Asymptotic, Orthogonal polynomial, Sharp rate bound, Special function, Uniform convergence
National Category
Mathematical Analysis
Identifiers
urn:nbn:se:ri:diva-56945 (URN)10.1007/s00365-021-09559-w (DOI)2-s2.0-85117708251 (Scopus ID)
Note
Funding details: Lunds Universitet; Funding details: Seventh Framework Programme, FP7, 248587; Funding text 1: This research was funded by the European Union FP7 research project THE, “The Hand Embodied,” under Grant Agreement 248587. The author is grateful for support by Prof. Henrik Jörntell of Lund University, Department of Experimental Medical Science.
2021-11-192021-11-192023-05-25Bibliographically approved