Paper Info
Title
Inequalities and asymptotics for the Euler–Mascheroni constant based on DeTemple’s result
Abstract
Let Rn=źk=1n1kźlnn+12$R_{n}={\\sum }_{k=1}^{n}\\frac {1}{k}-\\ln \\left (n+\\frac {1}{2}\\right )$. DeTemple proved the following inequality:124(n+1)2for all integers n ź 1, where ź denotes the Euler---Mascheroni constant. In this paper, we give a pair of recurrence relations for determining the constants aℓ and bℓ such thatRnźź~źℓ=1źaℓ(n2+n+bℓ)2ℓź1,nźź.$ R_{n}-\\gamma \\sim \\sum\\limits_{\\ell =1}^{\\infty }\\frac {a_{\\ell }}{(n^{2}+n+b_{\\ell })^{2\\ell -1}},\\qquad n\\to \\infty . $Based on this expansion, we establish some inequalities for the Euler---Mascheroni constant.
Year
DOI
Venue
2016
https://doi.org/10.1007/s11075-016-0116-9
Numerical Algorithms
Keywords
Field
DocType
Psi function,Euler–Mascheroni constant,Asymptotic formula,Inequality,Primary 33B15,Secondary 11Y60,41A60
Integer,Discrete mathematics,Asymptotic formula,Mathematical analysis,Recurrence relation,Asymptotic analysis,Mathematics,Euler–Mascheroni constant
Journal
Volume
Issue
ISSN
73
3
1017-1398
Citations 
PageRank 
References 
0
0.34
4
Authors
1
Name
Order
Citations
PageRank
Chao-Ping Chen15812.24