International Journal of Mathematics and Mathematical Sciences 
Volume 21 (1998), Issue 2, Pages 347-350
doi:10.1155/S0161171298000477

On real zeros of random polynomials with hyperbolic elements

K. Farahmand1 and M. Jahangiri2

 1Department of Mathematics, University of Ulster, Jordanstown, Co. Antrim, BT37 0QH, UK
2Department of Mathematics, Kent State University, 14111 Claridon Troy Road, Burton 44021-9500, OH, USA
Received 1 May 1996; Revised 30 December 1996

Abstract

This paper provides the asymptotic estimate for the expected number of real zeros of a random hyperbolic polynomial g1coshx+2g2cosh2x+…+ngncoshnx where gj,(j=1,2,…,n) are independent normally distributed random variables with mean zero and variance one. It is shown that for sufficiently large n this asymptotic value is (1/π)logn.