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- W3207996883 abstract "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 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." @default.
- W3207996883 created "2021-11-08" @default.
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- W3207996883 date "2021-10-23" @default.
- W3207996883 modified "2023-09-27" @default.
- W3207996883 title "On the Transition of Charlier Polynomials to the Hermite Function" @default.
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- W3207996883 doi "https://doi.org/10.1007/s00365-021-09559-w" @default.
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