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Higher order hypergeometric Lauricella function and zero asymptotics of orthogonal polynomials

✍ Scribed by P. Martínez-González; A. Zarzo

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
503 KB
Volume
233
Category
Article
ISSN
0377-0427

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✦ Synopsis

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.

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