Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An integral identity with applications in orthogonal polynomials   For $\boldsymbol{\large {\lambda}} = (\lambda_1,\ldots,\lambda_d)$ with
$\lambda_i > 0$, it is proved that \begin{equation*}
  \prod_{i=1}^d \frac{ 1}{(1- r x_i)^{\lambda_i}} =
\frac{\Gamma(|\boldsymbol{\large {\lambda}}|)}{\prod_{i=1}^{d}
\Gamma(\lambda_i)} \int_{\mathcal{T}^d} \frac{1}{ (1- r \langle x, u
\rangle)^{|\boldsymbol{\large {\lambda}}|}} \prod_{i=1}^d u_i^{\lambda_i-1} du,
\end{equation*} where $\mathcal{T}^d$ is the simplex in homogeneous coordinates
of $\mathbb{R}^d$, from which a new integral relation for Gegenbuer polynomials
of different indexes is deduced. The latter result is used to derive closed
formulas for reproducing kernels of orthogonal polynomials on the unit cube and
on the unit ball.

25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph