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arXiv · 1301.4771

Real zeros of 2F1 hypergeometric polynomials

D. Dominici·S. J. Johnston·K. Jordaan
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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.

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D. Dominici, S. J. Johnston, K. Jordaan. 2013-01-21. Real zeros of 2F1 hypergeometric polynomials. https://doi.org/10.1016/j.cam.2012.12.024

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