Asymptotic analysis of the Krawtchouk polynomials by the WKB method
Diego Dominici
Abstract
We analyze the Krawtchouk polynomials K(n,x,N,p,q) asymptotically. We use singular perturbation methods to analyze them for N large 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]x[0,N] involving some special functions. We give numerical examples showing the accuracy of our formulas.
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