APPELL'S FUNCTION F-1 AND EXTON'S TRIPLE HYPERGEOMETRIC FUNCTION X-9

In the theory of hypergeometric functions of one or several variables, a remarkable amount of mathematicians's concern has been given to develop their transformation formulas and summation identities. Here we aim at presenting explicit expressions (in a single form) of the following weighted Appell's function F-1: (1 + 2x)(-alpha) (1 + 2z)(-b) F-1 (c, a, b; 2c + j; 4x/1+ 2x, 4z/1 + 2z) (j = 0, +/- 1...,+/- 5) in terms of Exton's triple hypergeometric X-9. The results are derived with the help of generalizations of Kummer's second theorem very recently provided by Kim et al. A large number of very interesting special cases including Exton's result are also given.