Real zeros of 2F1 hypergeometric polynomials

Authors:
D. Dominici;S. J. Johnston;K. Jordaan
Affiliations:
Department of Mathematics, State University of New York at New Paltz, 1 Hawk Dr. Suite 9, New Paltz, NY 12561-2443, USA;Department of Mathematical Sciences, University of South Africa, PO Box 392, UNISA 0003, South Africa;Department of Mathematics and Applied Mathematics, University of Pretoria, Lynnwood Road, Pretoria, 0002, South Africa
Venue:
Journal of Computational and Applied Mathematics
Year:
2013

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Abstract

We use a method based on the division algorithm to determine all the values of the real parameters b and c for which the hypergeometric polynomials "2F"1(-n,b;c;z) have n real, simple zeros. Furthermore, we use the quasi-orthogonality of Jacobi polynomials to determine the intervals on the real line where the zeros are located.