Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Appell hypergeometric functions and classical separable mechanical
  systems   A relationship between two old mathematical subjects is observed: the theory
of hypergeometric functions and the separability in classical mechanics.
Separable potential perturbations of the integrable billiard systems and the
Jacobi problem for geodesics on an ellipsoid are expressed through the Appell
hypergeometric functions $F_4$ of two variables. Even when the number of
degrees of freedom increases, if an ellipsoid is symmetric, the number of
variables in the hypergeometric functions does not. Wider classes of separable
potentials are given by the obtained new formulae automaticaly.

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The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
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The categories of this paper are: q-fin
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The categories of this paper are: econ
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: q-alg