Transformation and summation formulas for double hypergeometric series (Q1372104)

The authors consider special double Kampé de Fériet functions \(F_{C:D;D'}^{A:B;B'} [1,1]\) with relations between parameters. Using known results and suitable manipulations, they obtain results of the following types. 1. Reductions: \(F_{1:1;p+1}^{0:3;p+3} [1,1]\) in terms of \(F_{1:1;p}^{0:3;p+2} [1,1]\), and several formulas for \(F_{1:1;2}^{0:3;4} [1,1]\) and \(F_{0:2;2}^{1:2;2} [1,1]\) in terms of \({}_4F_3 [1]\). 2. A transformation involving \(F_{1:1;1}^{0:3;3} [1,1]\) and \(F_{0:2;2}^{1:2;2} [1,1]\). 3. Several summation formulas for \(F_{1:1;1}^{0:3;3} [1,1]\) and \(F_{0:2;2}^{1:2;2} [1,1]\) in terms of gamma functions.