Geodesic
Transformation of the Triple Series of Gelfand, Graev, and Retakh into a Series of the Same Type and Related Problems
Matematičeskie zametki, Tome 89 (2011) no. 3, pp. 384-392

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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, computational methods.
Mots-clés : Radon transform 
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     author = {A. W. Niukkanen},
     title = {Transformation of the {Triple} {Series} of {Gelfand,} {Graev,} and {Retakh} into a {Series} of the {Same} {Type} and {Related} {Problems}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {384--392},
     publisher = {mathdoc},
     volume = {89},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2011_89_3_a7/}
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A. W. Niukkanen. Transformation of the Triple Series of Gelfand, Graev, and Retakh into a Series of the Same Type and Related Problems. Matematičeskie zametki, Tome 89 (2011) no. 3, pp. 384-392. http://geodesic.mathdoc.fr/item/MZM_2011_89_3_a7/