Inequalities for the gamma and polygamma functions
type: Item
instance of: scholarly article
title: Inequalities for the gamma and polygamma functions
zbMATH Open document ID: 0945.33003
DOI: 10.1007/BF02942573
author: Horst Alzer
published in: Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg
publication date: 2000-03-19T00:00:00Z
review text: Author offers an extension, with new proof, of a result by \textit{G. D. Anderson} and \textit{S.-L. Qiu} [Proc. Am. Math. Soc. 125, No. 11, 3355-3362 (1997; Zbl 0881.33001)] of the strict increasing of \(\log (\Gamma(x+1))/(x\log x),\) from \(]1,\infty[\) to \(]0,\infty[,\) furthermore inequalities for \(\psi^{(n)}(x+1)-\psi^{(n)}(x+s) (\psi=\Gamma'/\Gamma)\) with \(s\in]0,1[\) and for Euler's \(C=\lim_{n\to\infty} (\sum_{k=1}^n(1/k) - \log n)\).
Mathematics Subject Classification ID: 33B15
zbMATH DE Number: 1416669
zbMATH Keywords: gamma and psi functions
zbMATH Keywords: monotonicity
zbMATH Keywords: inequality
reviewed by: János Aczél
MaRDI profile type: Publication
cites work: Some Gamma Function Inequalities
cites work: On some inequalities for the gamma and psi functions
cites work: Inequalities for Zero-Balanced Hypergeometric Functions
cites work: A monotoneity property of the gamma function
cites work: Special functions of quasiconformal theory
cites work: Inequalities for quasiconformal mappings in space
cites work: Note on a paper by Uppuluri
cites work: On Gamma Function Inequalities
cites work: Leonhard Euler's Integral: A Historical Profile of the Gamma Function: In Memoriam: Milton Abramowitz
cites work: On Some Gamma Function Inequalities
cites work: The gamma function inequalities of Gurland and Gautschi
cites work: Some Elementary Inequalities Relating to the Gamma and Incomplete Gamma Function
cites work: A Stochastic Approach to the Gamma Function
cites work: Inequalities for the gamma function with applications to permanents
cites work: Q5627024
cites work: Some Extensions of W. Gautschi's Inequalities for the Gamma Function
cites work: Further Inequalities for the Gamma Function
cites work: Monotonicity results and inequalities for the gamma and error functions
cites work: Q4073667
cites work: Inequalities for ultraspherical polynomials and the gamma function
cites work: Q5659876
cites work: Logarithmic convexity and inequalities for the gamma function
cites work: Analytic Inequalities
cites work: Q4081596
cites work: 3295. Approximate evaluation of Euler’s constant
cites work: A Note on Gamma Functions
cites work: 75.9 Euler’s Constant
full work available at URL: https://doi.org/10.1007/bf02942573
OpenAlex ID: W1971234509
description: scientific article; zbMATH DE number 1416669