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

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.