eng
Science and Education Publishing
Turkish Journal of Analysis and Number Theory
2014-09-08
2
4
147
151
10.12691/tjant-2-4-8
TJANT2014248
article
A New Proof of an Inequality for the Logarithm of the Gamma Function and Its Sharpness
Mansour Mahmoud
mansour@mans.edu.eg
1
Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
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 is the Euler's constant, are the Bernoulli numbers and is the digamma function.
http://pubs.sciepub.com/tjant/2/4/8/tjant-2-4-8.pdf
Euler constant
* *ψ-function
harmonic numbers
inequalities
asymptotic expansion
sharp bounds