Asymptotics for a variant of the Mittag–Leffler function
By Stefan Gerhold. 2011
61 citations recorded by the source corpus.
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 the work by Le Roy [Valeurs asymptotiques de certaines séries procédant suivant les puissances entières et positives d’une variable réelle, Bull. des Sciences Math. 24, 1900] and Evgrafov [Asimptoticheskie otsenki i tselye funktsii, 3rd ed., Nauka, Moscow, 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.
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/1769b5f701e82279c7e5c4bee70e69a9a17fe6c0
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In Discrete Mathematics and Combinatorics
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Citations in the corpus
- Some Properties of the Kilbas-Saigo Function (2020, methodology): “An extension of this asymptotic behaviour was recently given in [9] for the so-called Mittag-Leffler functions of Le Roy type.”
- The Role of the Mittag-Leffler Function in Fractional Modeling (2015, methodology): “(18) Recently, the Le Roy-type function Equation (4), namely the function, has been introduced independently by Gerhold [40] and jointly by Garra and Polito [41].”
- A Note on Hadamard Fractional Differential Equations with Varying Coefficients and Their Applications in Probability (2017, methodology): “This function was independently introduced and studied by Gerhold in [11].”