Journal of Applied Mathematics and Stochastic Analysis
Volume 10 (1997), Issue 1, Pages 67-70

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

Copyright © 1997 J. Ernest Wilkins. 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.


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.