OKUBO TYPE DIFFERENTIAL EQUATIONS DERIVED FROM HYPERGEOMETRIC FUNCTIONS FD

Abstract

. From Lauricella’s hypergeometric functions in n variables, we construct a special type of Pfaffian equations of rank n + 1 called Okubo type differential equations. For each homogenized Okubo type differential equation, we construct special n + 1 coordinate functions called flat coordinate functions and an ( n + 1 ) -tuple of homogeneous functions called a potential vector.