Journal of Applied Mathematics and Stochastic Analysis 
Volume 5 (1992), Issue 4, Pages 307-313
doi:10.1155/S104895339200025X

Number of real roots of a random trigonometric polynomial

K. Farahmand

 University of Ulster, Department of Mathematics, Jordanstown, Co Antrim, BT37 0QB , United Kingdom
Received 1 December 1991; Revised 1 September 1992

Abstract

We study the expected number of real roots of the random equation g1cosθ+g2cos2θ+…+gncosnθ=K where the coefficients gj's are normally distributed, but not necessarily all identical. It is shown that although this expected number is independent of the means of gj, (j=1,2,…,n), it will depend on their variances. The previous works in this direction considered the identical distribution for the coefficients.