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Consider the systems (1) \ (sI-B){dv \over ds} = (\rho I-A)v and (2) \ {dx \over dt} = (B+t^{-1} A)x, where s and t are variables, ρ is a parameter, and A and B e diag(λ1,…,λn) are n by n matrices. (1) has only regular singular points, and (2) has an irregular singular point at t e ∞. Several kinds of special solutions having particular behavior near singular points were selected in previous papers. In the present paper, the author shows how (2) results from (1) in a process of confluence as ρ → ∞. It is analyzed how the special solutions of (1) converge to those of (2) in that process. As a consequence new proofs of earlier results about connection problems are obtained.