The higher order asymptotic expansion of the Krawtchouk polynomials
Classical Analysis and ODEs
2015-09-01 v1
Abstract
The paper extends the classical result on the convergence of the Krawtchouk polynomials to the Hermite polynomials. We provide the uniform asymptotic expansion in terms of the Hermite polynomials. We explicitly obtain expressions for a few initial terms of this expansion. The research is motivated by the study of ergodic sums of the Pascal adic transformation.
Keywords
Cite
@article{arxiv.1508.07421,
title = {The higher order asymptotic expansion of the Krawtchouk polynomials},
author = {Aleksei Minabutdinov},
journal= {arXiv preprint arXiv:1508.07421},
year = {2015}
}
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13 pages