Asymptotics of multiple orthogonal polynomials associated with the modified Bessel functions of the first kind

摘要

We consider polynomials which are orthogonal with respect to weight functions which are defined in terms of the modified Bessel functions Iν and Iν+1. These multiple orthogonal polynomials Pnν,c of type II were introduced earlier by the authors. The aim of this paper is to study some asymptotics of these polynomials, such as Plancherel–Rotach asymptotics. As a consequence of these results, we obtain the accumulation set of the scaled zeros of Pnν,c. We also give a Mehler–Heine-type formula for these polynomials which is valid on compact subsets of C. Hence, we obtain a more precise result about the asymptotic behavior of the small zeros of Pnν,c.