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Journal of Applied Mathematics and Stochastic Analysis
Volume 5, Issue 4, Pages 307-313
http://dx.doi.org/10.1155/S104895339200025X

Number of real roots of a random trigonometric polynomial

University of Ulster, Department of Mathematics, Jordanstown, Co Antrim, BT37 0QB , United Kingdom

Received 1 December 1991; Revised 1 September 1992

Copyright © 1992 Hindawi Publishing Corporation. 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.

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.