On a conjecture of Clark and Ismail
type: Item
instance of: scholarly article
title: On a conjecture of Clark and Ismail
zbMATH Open document ID: 1071.33004
author: Horst Alzer
author: Christian Berg
author: Stamatis Koumandos
published in: Journal of Approximation Theory
publication date: 2005-06-10T00:00:00Z
review text: In this paper the authors prove that there exists an integer \(m_0\) such that for all \(m\geq m_0\) the function \(\phi^{(m)}_m\) is not completely monotonic where \(\phi_m(x)=-x^m\psi^{(m)}(x)\) and \(\psi\) denotes the logarithmic derivative of Euler's gamma function. The findings of this paper disprove a conjecture of \textit{W. E. Clark} and \textit{M. E. H. Ismail} [Anal. Appl., Singap. 1, No.~1, 129--140 (2003; Zbl 1042.33002)].
reviewed by: P. K. Mital
Mathematics Subject Classification ID: 33B15
Mathematics Subject Classification ID: 33B30
Mathematics Subject Classification ID: 26A48
Mathematics Subject Classification ID: 26D07
zbMATH DE Number: 2174970
zbMATH Keywords: completely and absolutely monotonic-functions
zbMATH Keywords: inequalities
zbMATH Keywords: infinite series
zbMATH Keywords: polygamma functions
Wikidata QID: Q122861451
MaRDI profile type: Publication
full work available at URL: j.jat.2004.02.008
OpenAlex ID: W2068307085
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DOI: 10.1016/J.JAT.2004.02.008
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description: scientific article; zbMATH DE number 2174970