Asymptotic analysis of generalized Hermite polynomials

Details Asymptotic analysis of generalized Hermite polynomials Asymptotic analysis of generalized Hermite polynomials

2006-06-14

arxiv.org/abs/math/0606324v1

Mathematics

Classical Analysis and ODEs

28 pages, 6 figures

Scientific paper

We analyze the polynomials $H_{n}^{r}(x)$ considered by Gould and Hopper,
which generalize the classical Hermite polynomials. We present the main
properties of $H_{n}^{r}(x)$ and derive asymptotic approximations for large
values of $n$ from their differential-difference equation, using a discrete ray
method. We give numerical examples showing the accuracy of our formulas.

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