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Journal of Applied Mathematics and Stochastic Analysis
Volume 2006 (2006), Article ID 13980, 6 pages

Real zeros of random algebraic polynomials with binomial elements

1Faculty of Mathematics, Shahrood University of Technology, P.O. Box 316-36155, Shahrood, Iran
2Department of Mathematics, University of Ulster, Jordanstown Campus, County Antrim BT37 0QB, United Kingdom

Received 26 August 2005; Revised 26 September 2005; Accepted 26 September 2005

Copyright © 2006 A. Nezakati and K. Farahmand. 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 a0+a1x+a2x2++an1xn1. The coefficients aj(j=0,1,2,,n1) are assumed to be independent normal random variables with mean zero. For integers m and k=O(logn)2 the variances of the coefficients are assumed to have nonidentical value var(aj)=(k1jik), where n=km and i=0,1,2,,m1. Previous results are mainly for identically distributed coefficients or when var(aj)=(nj). We show that the latter is a special case of our general theorem.