Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A new form of the generalized complete elliptic integrals   Generalized trigonometric functions are applied to the Legendre-Jacobi
standard form of complete elliptic integrals, and a new form of the generalized
complete elliptic integrals of the Borweins is presented. According to the
form, it can be easily shown that these integrals have similar properties to
the classical ones. In particular, it is possible to establish a computation
formula of the generalized $\pi$ in terms of the arithmetic-geometric mean, in
the classical way as the Gauss-Legendre algorithm for $\pi$ by Salamin and
Brent. Moreover, an elementary new proof of Ramanujan's cubic transformation is
also given.

13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
26
The categories of this paper are: bayes-an