On the convergence of Charlier polynomials to the Hermite function

Details On the convergence of Charlier polynomials to the Hermite function On the convergence of Charlier polynomials to the Hermite function

2012-02-12

arxiv.org/abs/1202.2557v2

Mathematics

Classical Analysis and ODEs

14 pages, 1 figure; typos corrected; minor changes allow considerable strengthening of main theorem, also important for proof

Scientific paper

It is well known that Charlier polynomials converge to Hermite polynomials for integer values of the parameter that becomes the limiting polynomial degree. This is shown to generalize to real parameter values, in which case the limit becomes the Hermite function. Convergence is uniform in bounded intervals, and a sharp rate bound is proved. A corollary on the convergence of Charlier polynomial zeros to Hermite function zeros is given, including a rate bound.

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