Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A series solution of the general Heun equation in terms of incomplete
  Beta functions   We show that in the particular case when a characteristic exponent of the
singularity at infinity is zero the solution of the general Heun equation can
be expanded in terms of the incomplete Beta functions. By means of termination
of the series, closed-form solutions are derived for two infinite sets of the
involved parameters. These finite-sum solutions are written in terms of
elementary functions that in general are quasi-polynomials. The coefficients of
the expansion obey a three-term recurrence relation, which in some particular
cases may become two-term. We discuss the case when the recurrence relation
involves two non-successive terms and show that the coefficients of the
expansion are then calculated explicitly and the general solution of the Heun
equation is constructed as a combination of several hypergeometric functions
with quasi-polynomial pre-factors.

15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol