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Mat. Zametki, 2011, Volume 89, Issue 3, Pages 384–392 (Mi mz8370)  

Transformation of the Triple Series of Gelfand, Graev, and Retakh into a Series of the Same Type and Related Problems

A. W. Niukkanen

Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences

Abstract: A transformation of the triple series $T$ related to the Grassmanian $G_{2,4}$ into a series of the same structure type is obtained. This transformation generalizes the reduction formula of Gelfand, Graev, and Retakh taking the series $T$ to the Gauss function under two additional conditions and two more general reduction formulas taking the series $T$ to the Appell function $F_1$ and to the Horn function $G_2$ under one of the additional conditions. The approach used to analyze the series $T$ is based on the representation of the initial series $T$ in terms of series with convenient computational properties.

Keywords: Gaussian series, multiple hypergeometric series, symbolic fraction, Radon transform, computational methods

DOI: https://doi.org/10.4213/mzm8370

Full text: PDF file (469 kB)
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English version:
Mathematical Notes, 2011, 89:3, 374–381

Bibliographic databases:

Document Type: Article
UDC: 517.58
Received: 02.02.2009
Revised: 20.06.2010

Citation: A. W. Niukkanen, “Transformation of the Triple Series of Gelfand, Graev, and Retakh into a Series of the Same Type and Related Problems”, Mat. Zametki, 89:3 (2011), 384–392; Math. Notes, 89:3 (2011), 374–381

Citation in format AMSBIB
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