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Exponential asymptotics of the Mittag-Leffler function. (English) Zbl 1025.33009
The authors give a very detailed analysis of asymptotic behaviour (near infinity) of the Mittag-Leffler function E α,β , thereby putting special emphasis on possible occurrence of exponentially small additional terms after the algebraically decaying terms. They obtain uniform asymptotic expansions away from the Stokes lines, and furthermore they show the Stokes lines to be spirals if the parameter α is not real.
MSC:
33E12Mittag-Leffler functions and generalizations
41A60Asymptotic approximations, asymptotic expansions (steepest descent, etc.)