Journal of computational and applied mathematics vol:153 issue:1-2 pages:141-149
We consider polynomials which are orthogonal with respect to weight functions which are defined in terms of the modified Bessel functions I-nu and Inu+1. These multiple orthogonal polynomials P-n(nu,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 P-n(nu,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 P-n(nu,c). (C) 2002 Elsevier Science B.V. All rights reserved.