Turkish Journal of Analysis and Number Theory
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Turkish Journal of Analysis and Number Theory. 2014, 2(4), 147-151
DOI: 10.12691/tjant-2-4-8
Open AccessArticle

A New Proof of an Inequality for the Logarithm of the Gamma Function and Its Sharpness

Mansour Mahmoud1, 2,

1Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

2Department of Mathematics, Faculty of Science, Mansoura University, ansoura 35516, Egypt

Pub. Date: September 08, 2014

Cite this paper:
Mansour Mahmoud. A New Proof of an Inequality for the Logarithm of the Gamma Function and Its Sharpness. Turkish Journal of Analysis and Number Theory. 2014; 2(4):147-151. doi: 10.12691/tjant-2-4-8

Abstract

In the paper, the author shows that the partial sums are alternatively larger and smaller than the generalized Euler’s harmonic numbers with sharp bounds, where γ is the Euler's constant, are the Bernoulli numbers and ψ is the digamma function.

Keywords:
Euler constant ψ-function harmonic numbers inequalities asymptotic expansion sharp bounds

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