Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: New analytic continuations for the Appell $F_4$ series from quadratic
  transformations of the Gauss $_{2}F_1$ function   We present new analytic continuation formulas for the Appell
$F_4(a,b;c,d;x,y)$ double hypergeometric series where $d=a-b+1$, which allows
quadratic transformations of the Gauss ${}_2F_1$ hypergeometric function to be
used in the intermediate steps of the derivation. Such formulas are of
relevance to loop calculations of quantum field theory where they can been
used, for instance, to obtain new series representations of the two-loop
massive sunset Feynman diagram. The analytic continuation procedure introduced
in this paper is also sufficiently general so as to find uses elsewhere.

9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
34
The categories of this paper are: chem-ph
20
The categories of this paper are: acc-phys
32
The categories of this paper are: atom-ph
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs