The expected value of the number of real zeros of a random sum of Legendre polynomials期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

The expected value of the number of real zeros of a random sum of Legendre polynomials

Authors:	J Ernest Wilkins Jr

Institution:	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 $a_0\psi _0(t)+a_1\psi _1(t)+\dotsb +a_n\psi _n(t)$ , in which $\psi _k(t)$ 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 $3^{-1/2}n$ for large . We improve this result and show that this expected number is $3^{-1/2}n+o(n^\delta )$ for any positive $\delta$ .

Keywords:	Real zeros random polynomials Legendre polynomials

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文