  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.
