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We study the effect of the unfolding of a reducible double confluent Heun equation from the point of view of the Stokes phenomenon. We introduce a small complex parameter ε that splits together the non-resonant singular points x = 0 and x = ∞ into four different Fuchsian singularities x L = − ε , x R = ε , and x L L = − 1 / ε , x R R = 1 / ε , respectively. The perturbed equation is a symmetric general Heun equation and its general solution depends analytically on ε . Then we prove that when the perturbed equation has exactly two resonant singularities of different type, all the Stokes matrices of the initial double confluent Heun equation are realized as a limit of the upper-triangular parts of the monodromy matrices of the perturbed equation when ε → 0 . To establish this result we combine a direct computation with a theoretical approach. [ABSTRACT FROM AUTHOR]

We study an irregular singularity of Poincaré rank 1 at the origin of a certain third-order linear solvable homogeneous ODE. We perturb the equation by introducing a small parameter ε∈(ℝ+,0) (ε < 1), which causes the splitting of the irregular singularity into two finite Fuchsian singularities. We show that when the solutions of the perturbed equation contain logarithmic terms, the Stokes matrices of the initial equation are limits of the part of the monodromy matrices around the finite resonant Fuchsian singularities of the perturbed equation. [ABSTRACT FROM AUTHOR]