Zeros of the hypergeometric polynomial F(−n, b; c; z)
نویسنده
چکیده
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. AMS MOS Classification: 33C05, 30C15.
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