Higher order hypergeometric Lauricella function and zero asymptotics of orthogonal polynomials

[摘要] The asymptotic contracted measure of zeros of a large class of orthogonal polynomials is explicitly given in the form of a Lauricella function. The polynomials are defined by means of a three-term recurrence relation whose coefficients may be unbounded but vary regularly and have a different behaviour for even and odd indices. Subclasses of systems of orthogonal polynomials having their contracted measure of zeros of regular, uniform, Wigner, Weyl, Karamata and hypergeometric types are explicitly identified. Some illustrative examples are given. (C) 2009 Elsevier B.V. All rights reserved.

[发布日期] 2010-01-15

[效力级别]  Proceedings Paper

[关键词] Lauricella function;Orthogonal polynomials;Zeros;Asymptotics