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Asymptotic analysis of the Krawtchouk polynomials by the WKB method

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We analyze the Krawtchouk polynomials K n (x,N,p,q) asymptotically. We use singular perturbation methods to analyze them for N→∞, with appropriate scalings of the two variables x and n. In particular, the WKB method and asymptotic matching are used. We obtain asymptotic approximations valid in the whole domain [0,N]×[0,N], involving some special functions. We give numerical examples showing the accuracy of our formulas.

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  1. Department of Mathematics, State University of New York at New Paltz, 75 S. Manheim Blvd. Suite 9, New Paltz, NY, 12561-2443, USA

    Diego Dominici

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Dominici, D. Asymptotic analysis of the Krawtchouk polynomials by the WKB method. Ramanujan J 15, 303–338 (2008). https://doi.org/10.1007/s11139-007-9078-9

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