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.
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