Journal of Applied Mathematics and Stochastic Analysis 
Volume 15 (2002), Issue 1, Pages 83-88
doi:10.1155/S1048953302000084

Algebraic polynomials with random coefficients

K. Farahmand

 University of Ulster, Department of Mathematics, Co. Antrim, Jordanstown BT37 0QB, UK
Received 1 January 2001; Revised 1 June 2001

Abstract

This paper provides an asymptotic value for the mathematical expected number of points of inflections of a random polynomial of the form a0(ω)+a1(ω)(n1)1/2x+a2(ω)(n2)1/2x2+…an(ω)(nn)1/2xn when n is large. The coefficients {aj(w)}j=0n, w∈Ω are assumed to be a sequence of independent normally distributed random variables with means zero and variance one, each defined on a fixed probability space (A,Ω,Pr). A special case of dependent coefficients is also studied.