Some properties of multiple orthogonal polynomials associated with Macdonald functions

Abstract

Multiple orthogonal polynomials corresponding to two weights on [0,∞) associated with modified Bessel functions (Macdonald functions) K ν and K ν+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, n ) and ( A n+1, n , B n+1, n ) and for type II polynomials P n, n and P n+1, n . We also obtain generating functions for types I and II polynomials.