Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Algorithms to solve coupled systems of differential equations in terms
  of power series   Using integration by parts relations, Feynman integrals can be represented in
terms of coupled systems of differential equations. In the following we suppose
that the unknown Feynman integrals can be given in power series
representations, and that sufficiently many initial values of the integrals are
given. Then there exist algorithms that decide constructively if the
coefficients of their power series representations can be given within the
class of nested sums over hypergeometric products. In this article we will work
out the calculation steps that solve this problem. First, we will present a
successful tactic that has been applied recently to challenging problems coming
from massive 3-loop Feynman integrals. Here our main tool is to solve scalar
linear recurrences within the class of nested sums over hypergeometric
products. Second, we will present a new variation of this tactic which relies
on more involved summation technologies but succeeds in reducing the problem to
solve scalar recurrences with lower recurrence orders. The article will work
out the different challenges of this new tactic and demonstrates how they can
be treated efficiently with our existing summation technologies.

5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int