Holonomic systems of differential equations of rank two with singularities along Saito free divisors of simple type

摘要

We will show many examples of holonomic systems of three variables of rank two with singularities along Saito free divisors of simple type. Solutions of some of them are expressed in terms of elementary functions or hypergeometric functions. But some of the holonomic systems are difficult to solve. In the last section, we discuss the relationship between the holonomic systems obtained in this paper and algebraic solutions of Painlevé sixth equation.