CONFLUENCES OF APPELL'S F₂ SYSTEM OF HYPERGEOMETRIC DIFFERENTIAL EQUATIONS

抄録

We consider confluences of Euler-type integrals expressing solutions to Appell's F₂ system of hypergeometric differential equations, and study systems of confluent hypergeometric differential equations of rank four of two variables. Our consideration is based on a confluence transforming the abelian group (ℂ^×)² to the Jordan group of size two. For each system obtained by our study, we give its Pfaffian system with a connection matrix admitting a decomposition into four or five parts, each of which is the product of a matrix depending only on parameters and a rational 1-form in two variables. We classify these Pfaffian systems under an equivalence relation. Any system obtained by our study is equivalent to one of Humbert's Ψ₁ system, Humbert's Ξ₁ system, and the system satisfied by the product of two Kummer's confluent hypergeometric functions.