Geodesic
Linear Transformations and Reduction Formulas for the Gelfand Hypergeometric Functions Associated with the Grassmannians $G_{2,4}$ and $G_{3,6}$
Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 88-99 
A. W. Niukkanen; O. S. Paramonova. Linear Transformations and Reduction Formulas for the Gelfand Hypergeometric Functions Associated with the Grassmannians $G_{2,4}$ and $G_{3,6}$. Matematičeskie zametki, Tome 71 (2002) no. 1, pp. 88-99. http://geodesic.mathdoc.fr/item/MZM_2002_71_1_a7/
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     title = {Linear {Transformations} and {Reduction} {Formulas} for the {Gelfand} {Hypergeometric} {Functions} {Associated} with the {Grassmannians} $G_{2,4}$ and $G_{3,6}$},
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Voir la notice de l'article provenant de la source Math-Net.Ru

We show that the Gelfand hypergeometric functions associated with the Grassmannians $G_{2,4}$ and $G_{3,6}$ 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 $G_{2,4}$ (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 $H_2,G_2$, of the Appell functions $F_1,F_2,F_3$ and of the Gauss functions $F^2_1$, while the functions associated with the Grassmannian $G_{3,6}$ (the case of four variables) can be represented in terms of the series $G_2,F_1,F_2,F_3$ and$F^2_1$. 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.

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