Remark on a Mittag–Leffler function of Le Roy type
TLDR
In this article, the authors give necessary and sufficient conditions for complete monotonicity of a Mittag-Leffler function of Le Roy type on the negative half-line.Abstract:
We give some necessary and some sufficient conditions for the complete monotonicity on the negative half-line of a Mittag–Leffler function of Le Roy type. It is conjectured that the underlying posi...read more
Citations
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Journal ArticleDOI
Theory of Functions
TL;DR: In this paper, the authors pointed out that the distinction between "finite" and "infinite" is one which does not require definition, and that the authors' view is not the only accepted view.
Journal ArticleDOI
Series in Le Roy Type Functions: A Set of Results in the Complex Plane—A Survey
TL;DR: In this paper, an enumerable family of the Le Roy type functions is considered and the asymptotic formula for these special functions in the cases of large values of indices, that has been previously obtained, is provided.
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Multi-parametric Le Roy function
TL;DR: In this article , a multi-parametric generalization of the Le Roy function is introduced and studied from the point of view of an intermediate position between the Mittag-Leffler function and another important function of fractional calculus, namely the Wright function.
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On some geometric properties of the Le Roy-type Mittag-Leffler function
Khaled Mehrez,Sourav Das +1 more
TL;DR: In this paper , the authors considered the Le Roy-type Mittag-Leffler function and established sufficient conditions so that the normalized LeRoy type Mittag Leffler functions posses some geometric properties such as starlikeness, convexity, close-to-convexity (univalency) and uniformly convexness inside the unit disk.
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Multi-index le roy functions of mittag-leffler-prabhakar type
TL;DR: In this article , the authors introduce multi-index analogues of the Mittag-Leffler-Prabhakar type Le Roy functions (abbr. as multi-MLPR) with 4 m - indices.
References
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Higher Transcendental Functions
TL;DR: Higher Transcendental Functions Based on notes left by the late Prof. Harry Bateman, and compiled by the Staff of the Bateman Project as discussed by the authors, are presented in Table 1.
Book
Lévy Processes and Stochastic Calculus
TL;DR: In this paper, the authors present a general theory of Levy processes and a stochastic calculus for Levy processes in a direct and accessible way, including necessary and sufficient conditions for Levy process to have finite moments.
Journal ArticleDOI
Theory of Functions
TL;DR: In this paper, the authors pointed out that the distinction between "finite" and "infinite" is one which does not require definition, and that the authors' view is not the only accepted view.
Some classes of completely monotonic functions
Horst Alzer,Christian Berg +1 more
TL;DR: In this paper, it was shown that a polynomial of degree n > 1 with real coefficients is monotonic if and only if n = 1 and c 0 ≥ 11/12.
Journal ArticleDOI
Some classes of completely monotonic functions, II
Horst Alzer,Christian Berg +1 more
TL;DR: In this article, the gamma, digamma, and polygamma functions are defined in terms of the classical gamma functions, and a new class of completely monotonic functions is presented.