Strong asymptotics for Krawtchouk polynomials
The authors determine the strong asymptotics for Krawtchouk polynomials on the real line. They use their results to determine the distribution of the zeros of these polynomials \(p_n(nt;p,q)\) as \(n\to \infty)\). The polynomials \(p_n(n;p,q)\) being the Krawtchouk polynomial defined as \[ p_n(x;p,q): =\sum^n_{j=0} {x\choose j}{N-x \choose n-j}q^j(-p)^{n-j}; \] \(p,q \in(0,1)\) into \(p+q=1\) and \(N\in\mathbb{N}\), the set of positive integers into \(x\in \{0,1,\dots,N\}\).
scientific article; zbMATH DE number 1326432