Turán inequalities and complete monotonicity for a class of entire functions
type: Item
instance of: scholarly article
title: Turán inequalities and complete monotonicity for a class of entire functions
zbMATH Open document ID: 1499.26070
author: C. Bartholmé
author: Pierre Patie
published in: Analysis Mathematica
publication date: 2021-09-09T00:00:00Z
review text: The authors investigate analytical properties of the class of entire functions defined by \[ \mathcal{I}_\phi(t)=\sum_{n=0}^{\infty}\frac{1}{W_\phi(n+1)}\cdot\frac{t^n}{n!},\] where \(W_\phi(1)=1\), \(W_\phi(n+1)=\prod_{k=1}^{n}\phi(k)\) and \(\phi\) is a Bernstein function. Function \(\mathcal{I}_\phi\) with a certain \(\phi\) appeared in a paper of the second author [Ann. Inst. Henri Poincaré, Probab. Stat. 45, No. 3, 667--684 (2009; Zbl 1180.31010)].\par It was shown there that the function \(\mathcal{I}_\phi\) itself, or some of its transformations enjoy interesting analytical properties, such as complete monotonicity. \par In the present paper, the authors prove the properties mentioned above in a more general setting and derive additional ones. Their approach provides also new results for a wide range of special functions since the class of functions \(\mathcal{I}_\phi\) encompasses, as special instances, the modified Bessel functions, hypergeometric functions, the Mittag-Leffler functions, the Wright functions and \(q\)-series.
Mathematics Subject Classification ID: 26D10
Mathematics Subject Classification ID: 26A12
Mathematics Subject Classification ID: 33E12
zbMATH DE Number: 7393067
zbMATH Keywords: Turán inequality
zbMATH Keywords: complete monotonicity
zbMATH Keywords: entire function
zbMATH Keywords: Mittag-Leffler function
zbMATH Keywords: Bernstein function
zbMATH Keywords: self-similar operator
reviewed by: Petr Gurka
MaRDI profile type: Publication
full work available at URL: s10476-021-0088-4
OpenAlex ID: W3170205733
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DOI: 10.1007/S10476-021-0088-4
description: scientific article; zbMATH DE number 7393067