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

Source: [Zeros of the hypergeometric polynomial F(-n,b;c;z)](<https://www.sota2.com/research/paper/68fa4e131e209131ce9594ad>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:55:10.995Z

Authors: K Driver, K Jordaan

Published: 2008-12-03T13:02:43.000Z

## Abstract

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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/0812.0708>)

[PDF](<https://arxiv.org/pdf/0812.0708.pdf>)