Asymptotics for a Variant of the Mittag-Leffler Function

2011/03/11 by Stefan Gerhold, Gerhold, Stefan · 1 citation
Mathematics · #33E12 #41A60 #Combinatorics (math.CO) #Complex Variables (math.CV) #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematical functions and polynomials #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.1103.2285

openalex publication_date 2011/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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