Quadratic and cubic transformations and zeros of hypergeometric polynomials

Authors:
Kathy Driver;Manfred Möller
Affiliations:
John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa;John Knopfmacher Centre for Applicable Analysis and Number Theory, School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

Citing 3
Cited 1

Zeros of the hypergeometric polynomials F(—n,b;—2n;z)

Journal of Approximation Theory
Zeros of ultraspherical polynomials and the Hilbert-Klein formulas

Journal of Computational and Applied Mathematics
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,

Real zeros of 2F1 hypergeometric polynomials

Journal of Computational and Applied Mathematics

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Abstract

In this paper we consider the location of the zeros of the hypergeometric polynomials that lie in either the quadratic or the cubic class, where each of these classes is determined by a necessary and sufficient condition due to Kummer. We show that the zeros of most polynomials in these classes can be specified by simple applications of the results proved in recent papers of Driver and Duren.