Journal of Applied Mathematics and Stochastic Analysis 
Volume 10 (1997), Issue 1, Pages 67-70
doi:10.1155/S1048953397000063

Mean number of real zeros of a random trigonometric polynomial IV

J. Ernest Wilkins Jr.

 Clark Atlanta University, School of Arts and Science, Atlanta 30314, GA, USA
Received 1 September 1995; Revised 1 May 1996

Abstract

If aj(j=1,2,…,n) are independent, normally distributed random variables with mean 0 and variance 1, if p is one half of any odd positive integer except one, and if vnp is the mean number of zeros on (0,2π) of the trigonometric polynomial a1cosx+2pa2cos2x+…+npancosnx, then vnp=μp{(2n+1)+D1p+(2n+1)−1D2p+(2n+1)−2D3p}+O{(2n+1)−3}, in which μp={(2p+1)/(2p+3)}½, and D1p, D2p and D3p are explicitly stated constants.