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Matematicheskie Zametki, 2002, Volume 71, Issue 1, Pages 88–99
DOI: https://doi.org/10.4213/mzm330
(Mi mzm330)
 

This article is cited in 4 scientific papers (total in 4 papers)

Linear Transformations and Reduction Formulas for the Gelfand Hypergeometric Functions Associated with the Grassmannians G2,4 and G3,6

A. W. Niukkanen, O. S. Paramonova

Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences
Full-text PDF (223 kB) Citations (4)
References:
Abstract: We show that the Gelfand hypergeometric functions associated with the Grassmannians G2,4 and G3,6 with some special relations imposed on the parameters can be represented in terms of hypergeometric series of a simpler form. In particular, a function associated with the Grassmannian G2,4 (the case of three variables) can be represented (depending on the form of the additional conditions on the parameters of the series) in terms of the Horn series H2,G2, of the Appell functions F1,F2,F3 and of the Gauss functions F21, while the functions associated with the Grassmannian G3,6 (the case of four variables) can be represented in terms of the series G2,F1,F2,F3 andF21. The relation between certain formulas and the Gelfand–Graev–Retakh reduction formula is discussed. Combined linear transformations and universal elementary reduction rules underlying the method were implemented by a computer program developed by the authors on the basis of the computer algebra system Maple V-4.
Received: 08.10.1998
Revised: 08.07.2001
English version:
Mathematical Notes, 2002, Volume 71, Issue 1, Pages 80–89
DOI: https://doi.org/10.1023/A:1013978324286
Bibliographic databases:
UDC: 517.588+519.68
Language: Russian
Citation: A. W. Niukkanen, O. S. Paramonova, “Linear Transformations and Reduction Formulas for the Gelfand Hypergeometric Functions Associated with the Grassmannians G2,4 and G3,6”, Mat. Zametki, 71:1 (2002), 88–99; Math. Notes, 71:1 (2002), 80–89
Citation in format AMSBIB
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\by A.~W.~Niukkanen, O.~S.~Paramonova
\paper Linear Transformations and Reduction Formulas for the Gelfand Hypergeometric Functions Associated with the Grassmannians $G_{2,4}$ and $G_{3,6}$
\jour Mat. Zametki
\yr 2002
\vol 71
\issue 1
\pages 88--99
\mathnet{http://mi.mathnet.ru/mzm330}
\crossref{https://doi.org/10.4213/mzm330}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1900449}
\zmath{https://zbmath.org/?q=an:1027.33012}
\transl
\jour Math. Notes
\yr 2002
\vol 71
\issue 1
\pages 80--89
\crossref{https://doi.org/10.1023/A:1013978324286}
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Linking options:
  • https://www.mathnet.ru/eng/mzm330
  • https://doi.org/10.4213/mzm330
  • https://www.mathnet.ru/eng/mzm/v71/i1/p88
  • This publication is cited in the following 4 articles:
    1. A. W. Niukkanen, “Transformation of the Triple Series of Gelfand, Graev, and Retakh into a Series of the Same Type and Related Problems”, Math. Notes, 89:3 (2011), 374–381  mathnet  crossref  crossref  mathscinet  isi
    2. Niukkanen AW, “On the way to computerizable scientific knowledge (by the example of the operator factorization method)”, Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment, 502:2–3 (2003), 639–642  crossref  adsnasa  isi
    3. A.W. Niukkanen, “On the way to computerizable scientific knowledge (by the example of the operator factorization method)”, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 502:2-3 (2003), 639  crossref
    4. A. V. Niukkanen, “Kvadratichnye preobrazovaniya gipergeometricheskikh ryadov ot mnogikh peremennykh”, Fundament. i prikl. matem., 8:2 (2002), 517–531  mathnet  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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