Recursive calculation of connection formulas for systems of differential equations of Okubo normal form

TL;DR

This paper develops a recursive method to compute connection formulas for systems of differential equations in Okubo normal form, extending hypergeometric function techniques to higher-rank systems.

Contribution

It introduces a recursive approach to calculate connection coefficients for ONF systems using Euler integrals, linking higher-rank systems to lower-rank ones.

Findings

Derived recursive relations for connection coefficients.

Extended hypergeometric connection formulas to ONF systems.

Provided a systematic method for analytic continuation in ONF.

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.