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Zbl 1025.33009
Wong, R.; Zhao, Yu-Qiu
Exponential asymptotics of the Mittag-Leffler function. (English)
[J] Constructive Approximation 18, No.3, 355-385 (2002). ISSN 0176-4276; ISSN 1432-0940/e

The authors give a very detailed analysis of asymptotic behaviour (near infinity) of the Mittag-Leffler function $E_{\alpha,\beta}$, 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 $\alpha$ is not real.
[Rudolf Gorenflo (Berlin)]

MSC 2000:: *33E12 Mittag-Leffler functions and generalizations
41A60 Asymptotic problems in approximation

Keywords: Mittag-Leffler functions; exponential asymptotics; Stokes lines

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