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 λ_k ( k=1, 2,\ldots, n) of the diagonal matrix B satisfy ∣ λ_j − λ_k ∣ > ∣ λ_k ∣ > 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.

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