Multiple Orthogonal Polynomials Associated with the Modified Bessel Functions of the First Kind

Abstract

Abstract. We consider polynomials which are orthogonal with respect to weight functions, which are defined in terms of the modified Bessel function I _ν and which are related to the noncentral χ² -distribution. It turns out that it is the most convenient to use two weight functions with indices ν and ν+1 and to study orthogonality with respect to these two weights simultaneously. We show that the corresponding multiple orthogonal polynomials of type I and type II exist and give several properties of these polynomials (differential properties, Rodrigues formula, explicit formulas, recurrence relation, differential equation, and generating functions).