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Mat. Zametki, 2011 Volume 89, Issue 3, Pages 384–392 (Mi mzm8370)

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.

UDC: 517.58

Received: 02.02.2009
Revised: 20.06.2010

DOI: 10.4213/mzm8370


 English version:
Mathematical Notes, 2011, 89:3, 374–381

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© Steklov Math. Inst. of RAS, 2024