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Teoriya Veroyatnostei i ee Primeneniya, 2007, Volume 52, Issue 3, Pages 603–610
DOI: https://doi.org/10.4213/tvp81 (Mi tvp81) 		 
This article is cited in 5 scientific papers (total in 5 papers)

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On the polynomial analogue of the Chebyshev expansion

V. V. Senatov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (853 kB) Citations (5)
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DOI: https://doi.org/10.4213/tvp81
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
English version:
Theory of Probability and its Applications, 2008, Volume 52, Issue 3, Pages 531–538
DOI: https://doi.org/10.1137/S0040585X97983021
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. V. Senatov, “On the polynomial analogue of the Chebyshev expansion”, Teor. Veroyatnost. i Primenen., 52:3 (2007), 603–610; Theory Probab. Appl., 52:3 (2008), 531–538
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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