Hadamard expansions for integrals with saddles coalescing with an endpoint Original Research Article

Hadamard expansions are constructed for Laplace-type integrals containing a parameter and an asymptotic variable xx, which may be real or complex. These expansions yield a method of hyperasymptotic evaluation that remains valid throughout a range of the parameter corresponding to coalescence of a saddle point with an endpoint of the integration path. Numerical examples are given to illustrate the practical aspects of the computations.