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Transformation of the triple series of Gelfand, Graev, and Retakh into a series of the same type and related problems

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Abstract

A transformation of the triple series T related to the GrassmanianG 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.

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  1. Vernadsky Institute of Geochemistry and Analytical Chemistry, Russian Academy of Sciences, Moscow, Russia

    A. V. Niukkanen

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  1. A. V. Niukkanen
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Correspondence to A. V. Niukkanen.

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Original Russian Text © A. V. Niukkanen, 2011, published in Matematicheskie Zametki, 2011, Vol. 89, No. 3, pp. 384–392.

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Niukkanen, A.V. Transformation of the triple series of Gelfand, Graev, and Retakh into a series of the same type and related problems. Math Notes 89, 374–381 (2011). https://doi.org/10.1134/S0001434611030096

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  • DOI: https://doi.org/10.1134/S0001434611030096

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