Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Feynman integral in $\mathbb R^1\oplus\mathbb R^m$ and complex expansion
  of $_2F_1$   Closed form expressions are proposed for the Feynman integral
  $$
  I_{D, m}(p,q) = \int\frac{d^my}{(2\pi)^m}\int\frac{d^Dx}{(2\pi)^D}
  \frac1{(x-p/2)^2+(y-q/2)^4}
  \frac1{(x+p/2)^2+(y+q/2)^4}
  $$ over $d=D+m$ dimensional space with $(x,y),\,(p,q)\in \mathbb R^D \oplus
\mathbb R^m$, in the special case $D=1$. We show that $I_{1,m}(p,q)$ can be
expressed in different forms involving real and imaginary parts of the complex
variable Gauss hypergeometric function $_2F_1$, as well as generalized
hypergeometric $_2F_2$ and $_3F_2$, Horn $H_4$ and Appell $F_2$ functions.
Several interesting relations are derived between the real and imaginary parts
of $_2F_1$ and the function $H_4$.

9
The categories of this paper are: nlin
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
6
The categories of this paper are: astro-ph
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
35
The categories of this paper are: mtrl-th