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Consistent schemes for non-adiabatic dynamics derived from partial linearized density matrix propagation J. Chem. Phys. 137, 22A535 (2012) The spectral shift function and Levinson's theorem for quantum star graphs J. Math. Phys. 53, 082110 (2012) Explicit formulas for noncommutative deformations of PN and HN J. Math. Phys. 53, 073502 (2012) Coherent averaging in the frequency domain In order to determine the region where the Borel sum of a Wentzel-Kramers-Brillouin ͑WKB͒ solution of an mth order (mу3) ordinary differential equation Pϭ0 with polynomial coefficients is well defined, we apply the steepest descent method to the Laplace integral of a WKB solution of P ϭ0, with P denoting the Laplace transform of P. As a counterpart of the connection formula for , we introduce a new notion of the exact steepest descent path, which is the union of bifurcated steepest descent paths. Both theoretical and computer-assisted experimental studies are given to show the importance of this notion.

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