Exponential Asymptotics of the Mittag–Leffler Function

Abstract:

The Stokes lines/curves are identified for the Mittag–Leffler function

When α is not real, it is found that the Stokes curves are spirals. Away from the Stokes lines/curves, exponentially improved uniform asymptotic expansions are obtained. Near the Stokes lines/curves, Berry-type smooth transitions are achieved via the use of the complementary error function.