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).
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Coussement, Van Assche Multiple Orthogonal Polynomials Associated with the Modified Bessel Functions of the First Kind . Constr. Approx. 19, 237–263 (2003). https://doi.org/10.1007/s00365-002-0499-9
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DOI: https://doi.org/10.1007/s00365-002-0499-9