Uniform asymptotics and zeros of the associated Pollaczek polynomials

摘要

Using a difference-equation method in a previous paper, we study the associated Pollaczek polynomials Pn lambda(x;a,b,c) defined by a three-term recurrence relation. Two asymptotic approximations are derived for these polynomials; one holds for x=1+tn with -(a+b)0, and the other holds for x=1+tn with t in a neighborhood of t=-(a+b). An asymptotic formula is also provided for their largest zeros.