Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fractional Edgeworth Expansion: Corrections to the Gaussian-L\'evy
  Central Limit Theorem   In this article we generalize the classical Edgeworth expansion for the
probability density function (PDF) of sums of a finite number of symmetric
independent identically distributed random variables with a finite variance to
sums of variables with an infinite variance which converge by the generalized
central limit theorem to a L\'evy $\alpha$-stable density function. Our
correction may be written by means of a series of fractional derivatives of the
L\'evy and the conjugate L\'evy PDFs. This series expansion is general and
applies also to the Gaussian regime. To describe the terms in the series
expansion, we introduce a new family of special functions and briefly discuss
their properties. We implement our generalization to the distribution of the
momentum for atoms undergoing Sisyphus cooling, and show the improvement of our
leading order approximation compared to previous approximations. In vicinity of
the transition between L\'{e}vy and Gauss behaviors, convergence to asymptotic
results slows down.

26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex