ON THE THEORY OF HYPERGEOMETRIC FUNCTIONS IN TWO VARIABLES OF THE SECOND ORDER (Scientific journal of the Fergana State University, 2023)
In a well-known handbook on special function, there are misprints in the definitions of some functions included in the Horn List and inaccuracies in several systems of differential equations that some second-order hypergeometric functions of two variables allegedly satisfy. In this paper, on the basis of primary sources, the definitions of hypergeometric functions of two variables are defined, the truth of all systems of differential equations of the hypergeometric type is verified, with a detailed description of the process of compiling systems of partial differential equations.