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.
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
\Bibitem{NiuPar02}
\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
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\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:
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
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
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
A. V. Niukkanen, “Kvadratichnye preobrazovaniya gipergeometricheskikh ryadov ot mnogikh peremennykh”, Fundament. i prikl. matem., 8:2 (2002), 517–531