Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interbasis expansions in the Zernike system   The differential equation with free boundary conditions on the unit disk that
was proposed by Frits Zernike in 1934 to find Jacobi polynomial solutions
(indicated as I), serves to define a classical and a quantum system which have
been found to be superintegrable. We have determined two new orthogonal
polynomial solutions (indicated as II and III) that are separable, and which
involve Legendre and Gegenbauer polynomials.
  Here we report on their three interbasis expansion coefficients: between the
I--II and I--III bases they are given by $_3F_2(\cdots|1)$ polynomials that are
also special su($2$) Clebsch-Gordan coefficients and Hahn polynomials. Between
the II--III bases, we find an xpansion expressed by $_4F_3(\cdots|1)$'s and
Racah polynomials that are related to the Wigner $6j$ coefficients.

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The categories of this paper are: cond-mat
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The categories of this paper are: atom-ph
16
The categories of this paper are: stat
18
The categories of this paper are: econ
27
The categories of this paper are: comp-gas
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The categories of this paper are: physics
10
The categories of this paper are: q-bio
34
The categories of this paper are: chem-ph
33
The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol