On real zeros of random polynomials with hyperbolic elements
K. Farahmand1and M. Jahangiri2
Received01 May 1996
Revised30 Dec 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.