Geodesic
On the polynomial analogue of the Chebyshev expansion
Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 3, pp. 603-610

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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
Mots-clés : polynomial distributions. 
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     author = {V. V. Senatov},
     title = {On the polynomial analogue of the {Chebyshev} expansion},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {603--610},
     publisher = {mathdoc},
     volume = {52},
     number = {3},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2007_52_3_a10/}
}
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V. V. Senatov. On the polynomial analogue of the Chebyshev expansion. Teoriâ veroâtnostej i ee primeneniâ, Tome 52 (2007) no. 3, pp. 603-610. http://geodesic.mathdoc.fr/item/TVP_2007_52_3_a10/