Skip navigation
Please use this identifier to cite or link to this item:
Title: A harmonic mean inequality for the polygamma function
Authors: Das S.
Swaminathan, Anbhu
Published in: Mathematical Inequalities and Applications
Abstract: In this work, we discuss some new inequalities and a concavity property of the polygamma function ψ n (x) = ψ (x), x > 0, where ψ (x) represents the digamma function (i.e. logarithmic derivative of the gamma function Γ(x)). Using these inequalities, minimum value of harmonic mean of (−1) ψ n (x) and (−1) ψ n (1/x) is obtained in terms of the Riemann zeta function and the Bernoulli numbers. Further new characterizations of π and the Apéry’s constant are also presented as a consequence. ( ) dn n ( ) n ( ) dx n
Citation: Mathematical Inequalities and Applications(2020), 23(1): 71-76
Issue Date: 2020
Publisher: Element D.O.O.
Keywords: Harmonic mean
Monotonicity properties
Polygamma function
ISSN: 13314343
Author Scopus IDs: 56420537900
Author Affiliations: Das, S., Department of Mathematics, National Institute of Technology Jamshedpur, Jharkhand, 831014, India
Swaminathan, A., Department of Mathematics, Indian Institute of Technology, Roorkee, Uttarakhand 247667, India
Corresponding Author: Das, S.; Department of Mathematics, India; email:
Appears in Collections:Journal Publications [MA]

Files in This Item:
There are no files associated with this item.
Show full item record

Items in Repository are protected by copyright, with all rights reserved, unless otherwise indicated.