Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Laplace equation for the exterior of the Hankel contour and novel
  identities for hypergeometric functions   By employing conformal mappings, it is possible to express the solution of
certain boundary value problems for the Laplace equation in terms of a single
integral involving the given boundary data. We show that such explicit formulae
can be used to obtain novel identities for special functions. A convenient tool
for deriving this type of identities is the so-called \emph{global relation},
which has appeared recently in a wide range of boundary value problems. As a
concrete application, we analyze the Neumann boundary value problem for the
Laplace equation in the exterior of the so-called Hankel contour, which is the
contour that appears in the definition of both the gamma and the Riemann zeta
functions. By utilizing the explicit solution of this problem, we derive a
plethora of novel identities involving the hypergeometric function.

13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
1
The categories of this paper are: cs
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg