Communications of the
Korean Mathematical Society CKMS

A remarkably large number of special functions (such as the Gamma and Beta functions, the Gauss hypergeometric function, and so on) have been investigated by many authors. Motivated the works of both works of both Burchnall and Chaundy and Chaundy and very recently, Brychkov and Saad gave interesting generalizations of Appell type functions. In the present sequel to the aforementioned investigations and some of the earlier works listed in the reference, we present some new differential formulas for the generalized Appell's type functions $\kappa _{i},i=1,2,\ldots,18$ by considering the product of two $_{4}F_{3}$ functions.

Keywords: Appell's type functions, hypergeometric series, fractional calculus

MSC numbers: Primary 42C05; Secondary 33C45