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.
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
\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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\crossref{https://doi.org/10.4213/mzm330}
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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