Geodesic
A higher-order asymptotic expansion of the Krawtchouk polynomials
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXV, Tome 436 (2015), pp. 174-188

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The paper extends the classical result on the convergence of Krawtchouk polynomials to Hermite polynomials. We provide a uniform asymptotic expansion of Krawtchouk polynomials 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. 
@article{ZNSL_2015_436_a9,
     author = {A. R. Minabutdinov},
     title = {A higher-order asymptotic expansion of the {Krawtchouk} polynomials},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {174--188},
     publisher = {mathdoc},
     volume = {436},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_436_a9/}
}
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A. R. Minabutdinov. A higher-order asymptotic expansion of the Krawtchouk polynomials. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XXV, Tome 436 (2015), pp. 174-188. http://geodesic.mathdoc.fr/item/ZNSL_2015_436_a9/