Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Galois-theoretic proof of the differential transcendence of the
  incomplete Gamma function   We give simple necessary and sufficient conditions for the
$\frac{\partial}{\partial t}$-transcendence of the solutions to a parameterized
second order linear differential equation of the form \frac{\partial^2
Y}{\partial x^2} - p \frac{\partial Y}{\partial x} = 0, where $p\in F(x)$ is a
rational function in $x$ with coefficients in a $\frac{\partial}{\partial
t}$-field $F$. This result is crucial for the development of an efficient
algorithm to compute the parameterized Picard-Vessiot group of an arbitrary
parameterized second-order linear differential equation over $F(x)$. Our
criteria imply, in particular, the $\frac{\partial}{\partial t}$-transcendence
of the incomplete Gamma function $\gamma(t,x)$, generalizing a result of
Johnson, Reinhart, and Rubel [9].

5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con