The expected value of the number of real zeros of a random sum of Legendre polynomials
Authors:
J. Ernest Wilkins Jr.
Affiliation:
Department of Mathematics, Clark Atlanta University, Atlanta, Georgia 30314
Abstract:
It is known that the expected number of zeros in the interval of the sum , in which is the normalized Legendre polynomial of degree and the coefficients are independent normally distributed random variables with mean 0 and variance 1, is asymptotic to for large . We improve this result and show that this expected number is for any positive .