International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 63, Pages 3389-3395
Zeros of an algebraic polynomial with nonequal means random
Department of Mathematics, University of Ulster, Jordanstown BT37 0QB, County Antrim, UK
Received 16 July 2004
Copyright © 2004 K. Farahmand and P. Flood. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
This paper provides an asymptotic estimate for the expected number
of real zeros of a random algebraic polynomial . The coefficients
are assumed to be independent normal random
variables with nonidentical means. Previous results are mainly for
identically distributed coefficients. Our result remains valid
when the means of the coefficients are divided into many groups of
equal sizes. We show that the behaviour of the random polynomial
is dictated by the mean of the first group of the coefficients in
and the mean of the last group in .