Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sharp double inequality for complete elliptic integral of the first kind   For $r\in(0,1)$, the function $\K(r)=\int_0^{\pi/2}(1-r^2\sin^2t)^{-1/2}dt$
is known as the complete elliptic integral of the first kind. In this paper, we
prove the absolute monotonicity of two functions involving $\K(r)$. As a
consequence, we improve Alzer and Richards' result.

37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
24
The categories of this paper are: dg-ga
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ