Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Heun Functions and Some of Their Applications in Physics   Most of the theoretical physics known today is described by using a small
number of differential equations. For linear systems, different forms of the
hypergeometric or the confluent hypergeometric equations often suffice to
describe the system studied. These equations have power series solutions with
simple relations between consecutive coefficients and/ or can be represented in
terms of simple integral transforms. If the problem is nonlinear, one often
uses one form of the Painlev\'{e} equations. There are important examples,
however, where one has to use higher order equations. Heun equation is one of
these examples, which recently is often encountered in problems in general
relativity and astrophysics. Its special and confluent forms take names as
Mathieu, Lam\'{e} and Coulomb spheroidal equations. For these equations
whenever a power series solution is written, instead of a two-way recursion
relation between the coefficients in the series, we find one between three or
four different ones. An integral transform solution using simpler functions
also is not obtainable. The use of this equation in physics and mathematical
literature exploded in the later years, more than doubling the number of papers
with these solutions in the last decade, compared to time period since this
equation was introduced in 1889 up to 2008. We use SCI data to conclude this
statement, which is not precise, but in the correct ballpark. Here this
equation will be introduced and examples for its use, especially in general
relativity literature will be given.

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The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
34
The categories of this paper are: chem-ph
35
The categories of this paper are: mtrl-th
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat