A connection problem involving a logarithmic function

Abstract

A two points connection problem between two sets of fundamental solutions for a system of ordinary differential equations $tdX∕dt=(A+tB)X$ is studied under the assumptions that the eigenvalues ${\lambda }_k$ ($k=1,2,\dots ,n)$ of the diagonal matrix $B$ satisfy $\mid {\lambda }_j-{\lambda }_k\mid >\mid {\lambda }_k\mid >0$, and that the matrix $A$ has a pair of congruent eigenvalues. Connection coefficients are calculated by convergent series and error terms are reduced to be asymptotically zero.