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We consider a Pfaffian system expressing isomonodromy of an irregular systemof Okubo type, depending on complex deformation parameters u=(u_1,...,u_n),which are eigenvalues of the leading matrix at the irregular singuilarity. Atthe same time, we consider a Pfaffian system of non-normalized Schlesinger typeexpressing isomonodromy of a Fuchsian system, whose poles are the deformationparameters u_1,...,u_n. The parameters vary in a polydisc containing acoalescence locus for the eigenvalues of the leading matrix of the irregularsystem, corresponding to confluence of the Fuchsian singularities. We constructisomonodromic selected and singular vector solutions of the Fuchsian Pfaffiansystem together with their isomonodromic connection coefficients, so extendinga result of references [4] and [20] to the isomonodromic case, includingconfluence of singularities. Then, we introduce an isomonodromic Laplacetransform of the selected and singular vector solutions, allowing to obtainisomonodromic fundamental solutions for the irregular system, and their Stokesmatrices expressed in terms of connection coefficients. These facts, inaddition to extending [4] and [20] to the isomonodromic case withcoalescences/confluences, allow to prove by means of Laplace transform the mainresult of reference [11], which is the analytic theory of non-genericisomonodromic deformations of the irregular system with coalescing eigenvalues.

Isomonodromic Laplace Transform with Coalescing Eigenvalues and Confluence of Fuchsian Singularities