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A uniform asymptotic expansion for Krawtchouk polynomials. (English) Zbl 0963.33005
The Krawtchouk polynomials are considered for large values of the degree $n$. A uniform asymptotic expansion is derived, involving parabolic cylinder functions as main approximants. The expansion holds uniformly in certain domains of the parameters. The method is based on contour integrals for the polynomials and the saddle point method.

##### MSC:
 33C45 Orthogonal polynomials and functions of hypergeometric type 41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
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##### References:
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