This article is cited in 5 papers

Short Communications

On the polynomial analogue of the Chebyshev expansion

V. V. Senatov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: This paper proposes analogues of Chebyshev–Hermite polynomials for multidimensional spaces. These polynomials are polylinear functionals, which can be obtained by differentiating with respect to the Fréchet functions connected with densities of normal laws. It is shown how one can construct asymptotic expansions in the central limit theorem in the multidimensional case with the help of these polynomials.

Keywords: Chebyshev–Hermite polynomials, polylinear functionals, asymptotic expansions, central limit theorem, polynomial distributions.

Received: 27.12.2005

DOI: 10.4213/tvp81

 English version: Theory of Probability and its Applications, 2008, 52:3, 531–538

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