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Mathematics of the USSR-Izvestiya, 1990, Volume 35, Issue 3, Pages 543–571
DOI: https://doi.org/10.1070/IM1990v035n03ABEH000717 (Mi im1154) 		 
This article is cited in 21 scientific papers (total in 21 papers)

The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes. I

A. N. Varchenko
English version PDF (1736 kB) Citations (21)
References:
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DOI: https://doi.org/10.1070/IM1990v035n03ABEH000717
Abstract: When working with a set of linear functions and the configration of hyperplanes they define, one encounters a matrix of multidimensional hypergeometric integrals. We give a formula which expresses the determinant of this matrix in terms of critical values of the linear functions restricted to the configuration.
Bibliography: 26 titles.
Received: 26.04.1988
Russian version:
Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya, 1989, Volume 53, Issue 6, Pages 1206–1235
Bibliographic databases:
UDC: 517.95
MSC: Primary 14H05, 33A35; Secondary 05B30, 14K20, 35G20, 33A15
Language: English
Original paper language: Russian
Citation: A. N. Varchenko, “The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a configuration of hyperplanes. I”, Izv. Akad. Nauk SSSR Ser. Mat., 53:6 (1989), 1206–1235; Math. USSR-Izv., 35:3 (1990), 543–571
Citation in format AMSBIB
\Bibitem{Var89}
\by A.~N.~Varchenko
\paper The Euler beta-function, the Vandermonde determinant, Legendre's equation, and critical values of linear functions on a~configuration of hyperplanes.~I
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1989
\vol 53
\issue 6
\pages 1206--1235
\mathnet{http://mi.mathnet.ru/im1154}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1039962}
\zmath{https://zbmath.org/?q=an:0709.33001|0695.33004}
\transl
\jour Math. USSR-Izv.
\yr 1990
\vol 35
\issue 3
\pages 543--571
\crossref{https://doi.org/10.1070/IM1990v035n03ABEH000717}
Linking options:
  • https://www.mathnet.ru/eng/im1154
  • https://doi.org/10.1070/IM1990v035n03ABEH000717
  • https://www.mathnet.ru/eng/im/v53/i6/p1206
    • This publication is cited in the following 21 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:1988
    Russian version PDF:1147
    English version PDF:35
    References:103
    First page:5
     
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