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Algebraic polynomials with random coefficients

By K. Farahmand

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

Topics: number of real roots, random algebraic polynomials, Kac-Rice formula, random variables, points of inflection., Science, Q, Mathematics, QA1-939
Publisher: Hindawi Limited
Year: 2002
DOI identifier: 10.1155/S1048953302000084
OAI identifier: oai:doaj.org/article:4760656995d1405dbcc0a2fd1ad35351
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