Computational Methods and Function Theory 1 (2001), No. 1, 275--287
Copyright Heldermann Verlag 2001
Kathryn Boggs
kboggs@umich.edu, Department of Mathematics, Undergraduate Programs Office, University of Michigan, Ann Arbor, Michigan 48109--1109, U.S.A.
Peter Duren
duren@umich.edu, Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109--1109, U.S.A.
For certain ranges of parameters, it is shown that the hypergeometric function $F(a,b;b+1;z)$ has no zeros in a specified half-plane. It is also shown that the zeros of the hypergeometric polynomials $$ F(-n,kn+\ell+1;kn+\ell+2;z) $$ cluster on one loop of a specified lemniscate. Other results then follow from quadratic relations.
Keywords: Hypergeometric functions, hypergeometric polynomials, Jacobi polynomials, zeros, Euler integral, asymptotic curves.
MSC 2000: 33C05, 30C15, 33C45.
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