Zeros of the hypergeometric polynomials F(-n, b;-2n; z)

We investigate the location of dir zeros of the hypergeometric polynomial F (-n, b; -2n; z) for b real. The Hilbert-Klein formulas are used to specify the number of real zeros in the intervals (- infinity, 0), (0, 1), or (1, i nfinity). For b > 0 we obtain the equation of the Cassini curve which the z eros of w(n)F(-n, b: -2n, 1/w) approach as n --> infinity and thereby prove a special case of a conjecture made by Martinez-Finkelshtein, Martinez-Gon zalez, and Orive. We also present some numerical evidence linking the zeros of F with more general Cassini curves. (C) 2001 Academic Press.