Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp bounds for harmonic numbers   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.

12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
13
The categories of this paper are: quant-ph
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex