Zeros of the hypergeometric polynomial F(-n,b;c;z)

Details Zeros of the hypergeometric polynomial F(-n,b;c;z) Zeros of the hypergeometric polynomial F(-n,b;c;z)

2008-12-03

arxiv.org/abs/0812.0708v1

Algorithms for Approximation IV, Proceedings of the 2001 International Symposium: 436-445

Mathematics

Classical Analysis and ODEs

Scientific paper

Our interest lies in describing the zero behaviour of Gauss hypergeometric polynomials $F(-n,b; c; z)$ where $b$ and $c$ are arbitrary parameters. In general, this problem has not been solved and even when $b$ and $c$ are both real, the only cases that have been fully analyzed impose additional restrictions on $b$ and $c$. We review recent results that have been proved for the zeros of several classes of hypergeometric polynomials $F(-n,b; c; z)$ where $b$ and $c$ are real. We show that the number of real zeros of $F(-n,b; c; z)$ for arbitrary real values of the parameters $b$ and $c$, as well as the intervals in which these zeros (if any) lie, can be deduced from corresponding results for Jacobi polynomials.

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