CHAPTER 5 - The Number and Expected Number of Real Zeros of Other Random Polynomials

Abstract

This chapter discusses random polynomials other than algebraic, that is, random trigonometric polynomials, random orthogonal polynomials, and random hyperbolic polynomials. It explains the relationship between random algebraic polynomials and other types of random polynomials. Any random orthogonal polynomial can be written as a random algebraic polynomial using known polynomial representations of orthogonal polynomials. The chapter also describes the number and expected number of real zeros of random trigonometric polynomials. It then discusses random hyperbolic polynomials and the expected number of real zeros of these polynomials. The chapter discusses the average number of real zeros of random orthogonal polynomials. It presents some numerical results on the number of real zeros of the random polynomials considered in the chapter and some figures that illustrate the distribution of the real zeros of the random polynomials considered here.