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 Mat. Zametki, 2002, Volume 71, Issue 1, Pages 88–99 (Mi mz330)

Linear Transformations and Reduction Formulas for the Gelfand Hypergeometric Functions Associated with the Grassmannians $G_{2,4}$ and $G_{3,6}$

A. W. Niukkanen, O. S. Paramonova

Abstract: We show that the Gelfand hypergeometric functions associated with the Grassmannians $G_{2,4}$ and $G_{3,6}$ 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 $G_{2,4}$ (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 $H_2,G_2$, of the Appell functions $F_1,F_2,F_3$ and of the Gauss functions $F^2_1$, while the functions associated with the Grassmannian $G_{3,6}$ (the case of four variables) can be represented in terms of the series $G_2,F_1,F_2,F_3$ and$F^2_1$. 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.

DOI: https://doi.org/10.4213/mzm330

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English version:
Mathematical Notes, 2002, 71:1, 80–89

Bibliographic databases:

UDC: 517.588+519.68
Revised: 08.07.2001

Citation: A. W. Niukkanen, O. S. Paramonova, “Linear Transformations and Reduction Formulas for the Gelfand Hypergeometric Functions Associated with the Grassmannians $G_{2,4}$ and $G_{3,6}$”, Mat. Zametki, 71:1 (2002), 88–99; Math. Notes, 71:1 (2002), 80–89

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz330
• https://doi.org/10.4213/mzm330
• http://mi.mathnet.ru/eng/mz/v71/i1/p88

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This publication is cited in the following articles:
1. A. V. Niukkanen, “Kvadratichnye preobrazovaniya gipergeometricheskikh ryadov ot mnogikh peremennykh”, Fundament. i prikl. matem., 8:2 (2002), 517–531
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
3. 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
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