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 ${}_2F_1(\alpha, \beta, \gamma; x)$ 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.