Multiple Orthogonal Polynomials Associated with the Modified Bessel Functions of the First Kind |
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Authors: | Coussement and Van Assche |
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Institution: | (1) Department of Mathematics Katholieke Universiteit Leuven Celestijnenlaan 200B B-3001 Leuven Belgium, BE;(2) Department of Mathematics Katholieke Universiteit Leuven Celestijnenlaan 200B B-3001 Leuven Belgium walter@wis.kuleuven.ac.be, BE |
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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 χ
2
-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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Keywords: | , Multiple orthogonal polynomials, Hermite—,Padé approximation, Modified Bessel functions, AMS Classification, 33C10,,,,,,33C45, 41A28, 42C05, |
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