Some properties of multiple orthogonal polynomials associated with Macdonald functions

摘要

Multiple orthogonal polynomials corresponding to two weights on [0,∞) associated with modified Bessel functions (Macdonald functions) Kν and Kν+1 were introduced in Van Assche, Yakubovich (Integral Transforms Special Funct. 9 (2000) 229–244) and recently also studied by Ben Cheikh, Douak (Meth. Appl. Anal., to appear). We obtain explicit formulas for type I vector polynomials (An,n,Bn,n) and (An+1,n,Bn+1,n) and for type II polynomials Pn,n and Pn+1,n. We also obtain generating functions for types I and II polynomials.