Asymptotics for a Variant of the Mittag-Leffler Function
Complex Variables
2011-03-14 v1 Combinatorics
Abstract
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.
Cite
@article{arxiv.1103.2285,
title = {Asymptotics for a Variant of the Mittag-Leffler Function},
author = {Stefan Gerhold},
journal= {arXiv preprint arXiv:1103.2285},
year = {2011}
}