Sharp bounds for harmonic numbers

Details Sharp bounds for harmonic numbers Sharp bounds for harmonic numbers

2010-02-20

arxiv.org/abs/1002.3856v1

Bai-Ni Guo and Feng Qi, Applied Mathematics and Computation 218 (2011), no. 3, 991-995

Mathematics

Classical Analysis and ODEs

7 pages

Scientific paper

10.1016/j.amc.2011.01.089

In the paper, we first survey some results on inequalities for bounding harmonic numbers or Euler-Mascheroni constant, and then we establish a new sharp double inequality for bounding harmonic numbers as follows: For $n\in\mathbb{N}$, the double inequality -\frac{1}{12n^2+{2(7-12\gamma)}/{(2\gamma-1)}}\le H(n)-\ln n-\frac1{2n}-\gamma<-\frac{1}{12n^2+6/5} is valid, with equality in the left-hand side only when $n=1$, where the scalars $\frac{2(7-12\gamma)}{2\gamma-1}$ and $\frac65$ are the best possible.

Affiliated with

Also associated with

No associations

Rating

Sharp bounds for harmonic numbers does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Sharp bounds for harmonic numbers, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Sharp bounds for harmonic numbers will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-692457