Colloquium Announcement
Department of Mathematics
West Virginia University
for
Thursday, January 21, 1999, at 3:45pm
in 315 Armstrong Hall
(Tea and cookies begin at 3:00 in coffee room.)
Professor James Ridley
University of the Witwatersrand, Johannesburg, South Africa
VISITING PROFESSOR at WWU (math dept) IN SPRING 1999
Location of the zeros of some hypergeometric polynomials
The talk will be suitable for a general audience.
Students are strongly encouraged to participate.
Abstract
Evidence obtained from Mathematica plots indicates
that, for non-zero b>-0.5, the zeros of the hypergeometric function
2F1(-n,b,2b;z), which is a polynomial of
degree n, all lie on the circle |z-1|=1. We give an
elementary proof of this result, in three stages:
firstly finding a neat expression for
2F1(-n,b,2b;w+1),
secondly showing that its zeros can be expressed in terms of those of
the n-th derivative of (1+x2)-b,
and thirdly proving that, for non-zero b>-0.5, all the latter zeros
lie on the real line.
The information on the future (and past) Colloquia can be also found on web at the
address:
http://www.math.wvu.edu/homepages/kcies/colloquium.html