The paper extends a classical result on the convergence of the Krawtchouk polynomials to the Hermite polynomials. We provide a uniform asymptotic expansion in terms of Hermite polynomials and obtain explicit expressions for a few first terms of this expansion. The research is motivated by the study of ergodic sums of the Pascal adic transformation. Bibliography: 10 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 436, 2015, pp. 174–188.
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Minabutdinov, A.R. A Higher Order Asymptotic Expansion of the Krawtchouk Polynomials. J Math Sci 215, 738–747 (2016). https://doi.org/10.1007/s10958-016-2879-x
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DOI: https://doi.org/10.1007/s10958-016-2879-x