Previous article Next article A Harmonic Mean Inequality for the Gamma FunctionWalter GautschiWalter Gautschihttps://doi.org/10.1137/0505030PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractWe prove that the harmonic mean of $\Gamma (x)$ and $\Gamma (1/ x)$ is greater than or equal to $\Gamma (1) = 1$ for arbitrary $x > 0$. Previous article Next article FiguresRelatedReferencesCited ByDetails A harmonic mean inequality for the q-gamma functionThe Ramanujan Journal, Vol. 58, No. 4 | 9 August 2021 Cross Ref Harmonic Mean Inequalities for Hyperbolic FunctionsEarthline Journal of Mathematical Sciences | 17 January 2021 Cross Ref On the Erlang loss functionActa Mathematica Hungarica, Vol. 162, No. 1 | 30 June 2020 Cross Ref BibliographyZeta and q-Zeta Functions and Associated Series and Integrals | 1 Jan 2012 Cross Ref The schur convexity of gini mean values in the sense of harmonic meanActa Mathematica Scientia, Vol. 31, No. 3 | 1 May 2011 Cross Ref A Sharp Double Inequality between Harmonic and Identric MeansAbstract and Applied Analysis, Vol. 2011 | 1 Jan 2011 Cross Ref New approximation formulas for evaluating the ratio of gamma functionsMathematical and Computer Modelling, Vol. 52, No. 1-2 | 1 Jul 2010 Cross Ref A Double Inequality for Gamma FunctionJournal of Inequalities and Applications, Vol. 2009, No. 1 | 1 Jan 2009 Cross Ref Gamma function inequalitiesNumerical Algorithms, Vol. 49, No. 1-4 | 15 March 2008 Cross Ref Connection factors in the Schrödinger equation with a polynomial potentialJournal of Computational and Applied Mathematics, Vol. 207, No. 2 | 1 Oct 2007 Cross Ref Inequalities involving Γ(x) and Γ(1/x)Journal of Computational and Applied Mathematics, Vol. 192, No. 2 | 1 Aug 2006 Cross Ref On Gautschi's harmonic mean inequality for the gamma functionJournal of Computational and Applied Mathematics, Vol. 157, No. 1 | 1 Aug 2003 Cross Ref Inequalities and monotonicity properties for the gamma functionJournal of Computational and Applied Mathematics, Vol. 133, No. 1-2 | 1 Aug 2001 Cross Ref A harmonic mean inequality for the gamma functionJournal of Computational and Applied Mathematics, Vol. 87, No. 2 | 1 Dec 1997 Cross Ref Inequalities and Monotonicity Properties for Gamma and q-Gamma FunctionsApproximation and Computation: A Festschrift in Honor of Walter Gautschi | 1 Jan 1994 Cross Ref Some Mean Value Inequalities for the Gamma FunctionWalter GautschiSIAM Journal on Mathematical Analysis, Vol. 5, No. 2 | 17 February 2012AbstractPDF (700 KB) Volume 5, Issue 2| 1974SIAM Journal on Mathematical Analysis159-349 History Submitted:24 May 1972Published online:17 February 2012 InformationCopyright © 1974 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0505030Article page range:pp. 278-281ISSN (print):0036-1410ISSN (online):1095-7154Publisher:Society for Industrial and Applied Mathematics