Some properties of multiple orthogonal polynomials associated with Macdonald functions

Multiple orthogonal polynomials corresponding to two weights on [0,infinity) associated with modified Bessel functions (Macdonald functions) K-v and Kv+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 (A(n.n),B-n,B-n) and (A(n+1.n),B-n+1,B-n) and for type II polynomials P-n.n and P-n+1,P-n. We also obtain generating functions for types I and II polynomials. (C) 2001 Elsevier Science B.V. All rights reserved.