The problems of definitions and symbols of G- and H-functions of several variables

Abstract

In the present paper some problems concerned with the notations used in the theory of G- and H-functions of several variables are considered. The G- and H-functions of several variables are defined and the definitions include all the known ones of the type. For designation of these functions some symbols are suggested, which are very simple or complete for description of the function dependence on a large number of parameters. In one of the symbols ternary calculus is used. Different particular cases of G- and H-functions are examined, sufficient conditions of their existence and some of their properties are presented, and for G-functions the appropriate partial differential equation and a certain set of its solutions are given.