Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lagrange inversion formula, Laguerre polynomials and the free unitary
  Brownian motion   This paper is devoted to the computations of some relevant quantities
associated with the free unitary Brownian motion. Using the Lagrange inversion
formula, we first derive an explicit expression for its alternating star
cumulants of even lengths and relate them to those having odd lengths by means
of a summation formula for the free cumulants with product as entries. Next, we
use again this formula together with a generating series for Laguerre
polynomials in order to compute the Taylor coefficients of the reciprocal of
the $R$-transform of the free Jacobi process associated with a single
projection of rank $1/2$ and those of the $S$-transform as well. This
generating series lead also to the Taylor expansions of the Schur function of
the spectral distribution of the free unitary Brownian motion and of its first
iterate.

18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
12
The categories of this paper are: nucl-th
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-fin
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The categories of this paper are: eess
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc