Asymptotics for a Variant of the Mittag-Leffler Function

Details Asymptotics for a Variant of the Mittag-Leffler Function Asymptotics for a Variant of the Mittag-Leffler Function

2011-03-11

arxiv.org/abs/1103.2285v1

Mathematics

Complex Variables

Scientific paper

We generalize the Mittag-Leffler function by attaching an exponent to its Taylor coefficients. The main result is an asymptotic formula valid in sectors of the complex plane, which extends work by Le Roy [Bull. des sciences math. 24, 1900] and Evgrafov [Asimptoticheskie otsenki i tselye funktsii, 1979]. It is established by Plana's summation formula in conjunction with the saddle point method. As an application, we (re-)prove a non-holonomicity result about powers of the factorial sequence.

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