Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Mehler's formulas for the univariate complex Hermite polynomials and
  applications   We give two widest Mehler's formulas for the univariate complex Hermite
polynomials $H_{m,n}^\nu$, by performing double summations involving the
products $u^m H_{m,n}^\nu (z,\overline{z}) \overline{H_{m,n}^\nu
(w,\overline{w})}$ and $u^m v^n H_{m,n}^\nu (z,\overline{z})
\overline{H_{m,n}^{\nu'} (w,\overline{w})}$. They can be seen as the complex
analogues of the classical Mehler's formula for the real Hermite polynomials.
The proof of the first one is based on a generating function giving rise to the
reproducing kernel of the generalized Bargmann space of level $m$. The second
Mehler's formula generalizes the one appearing as a particular case of the
so-called Kibble-Slepian formula. The proofs, we present here are direct and
more simpler. Moreover, direct applications are given and remarkable identities
are derived.

28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
3
The categories of this paper are: physics
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ