Recursive Calculation of Connection Formulas for Systems of Differential Equations of Okubo Normal Form

Abstract

We study the structure of analytic continuation of solutions of an even rank system of linear ordinary differential equations of Okubo normal form (ONF). We develop an adjustment of the method by using the Euler integral for evaluating the connection formulas of the Gauss hypergeometric function 2F1(α, β, γ; x) to the system of ONF. We obtain recursive relations between connection coefficients for the system of ONF and ones for the underlying system of half rank.

Connection Coefficients and Monodromy Representations for a Class of Okubo Systems of Ordinary Differential Equations

“…Our argument is based on the fact that the permutaion of characteristic exponents at a singular point can be realized by the adjoint action of a contant matrix. We remark that our approach is similar to that of Yokoyama [14] in which recursive relations for connection coe‰cients are investigated in the framework of extending operations for Okubo systems. It is not clear, however, whether the connection coe‰cients for individual Okubo systems in Yokoyama's list can be directly determined only from the results of [14].…”

“…We remark that our approach is similar to that of Yokoyama [14] in which recursive relations for connection coefficients are investigated in the framework of extending operations for Okubo systems. It is not clear, however, whether the connection coefficients for individual Okubo systems in Yokoyama's list can be directly determined only from the results of [14]. We also remark that the connection problem for rigid irreducible Fuchsian differential equations of scalar type has been discussed by Oshima [9] as an application of the Katz operations.…”