Number of real roots of a random trigonometric polynomial. (1992) - Farahmand, K.
Abstract : We study the expected number of real roots of the random equation g 1 cos θ + g 2 cos 2 θ + … + g n cos n θ = K where the coefficients g j 's are normally distributed, but not necessarily all identical. It is shown that although this expected number is independent of the means of g j, ( j = 1, 2, …, n ), it will depend on their variances. The previous works in this direction considered the identical distribution for the coefficients.