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- W4298407906 abstract "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 for instance in queueing theory. It is shown in this paper that the convergence is uniform in bounded intervals, and a sharp rate bound is proved. It is also 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. While rigorous, the proofs use only elementary techniques." @default.
- W4298407906 created "2022-10-02" @default.
- W4298407906 creator A5016808355 @default.
- W4298407906 date "2012-02-12" @default.
- W4298407906 modified "2023-09-26" @default.
- W4298407906 title "On the transition of Charlier polynomials to the Hermite function" @default.
- W4298407906 doi "https://doi.org/10.48550/arxiv.1202.2557" @default.
- W4298407906 hasPublicationYear "2012" @default.
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