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Mathematics > Complex Variables

Title:Integral representations and asymptotic behaviour of a Mittag-Leffler type function of two variables

Authors:Christian Lavault (LIPN)
Abstract: Integral representations play a prominent role in the analysis of entire functions. The representations of generalized Mittag-Leffler type functions and their asymptotics have been (and still are) investigated by plenty of authors in various conditions and cases.The present paper explores the integral representations of a special function extending to two variables the two-parametric Mittag-Leffler type function. Integral representations of this functions within different variation ranges of its arguments for certain values of the parameters are thus obtained. Asymptotic expansion formulas and asymptotic properties of this function are also established for large values of the variables. This yields corresponding theorems providing integral representations as well as expansion formulas.
Comments: 2nde version de l'article d\'epos\'e sur Hal et arXiv en mai 2017 , sous presse \`a Advances in Operator Theory (AOT). arXiv admin note: substantial text overlap with arXiv:1705.05562
Subjects: Complex Variables (math.CV); Classical Analysis and ODEs (math.CA); Functional Analysis (math.FA)
Journal reference: Adv. Oper. Theory, Tusi Mathematical Research Group, A Para\^itre, 3 (2), pp.40--48
DOI: 10.22034/aot.1705-1167
Cite as: arXiv:1710.10839 [math.CV]
  (or arXiv:1710.10839v1 [math.CV] for this version)

Submission history

From: Christian Lavault [view email]
[v1] Mon, 30 Oct 2017 10:00:52 UTC (9 KB)