Zeros of hypergeometric polynomials

Abstract

There is a natural connection between hypergeometric polynomials F(-n,b;c;z) and Jacobi polynomials. For special choices of the real parameters b and c, this connection can be exploited to furnish quite complete information on the location of the zeros of F. The class of hypergeometric polynomials that admit a quadratic transformation is discussed in detail. For general real b and c, the Hilbert-Klein formulas yield information on the numbers and location of non-complex zeros while the complex zeros lie on curves whose equations are not yet known.