Authors: Dragović, Vladimir 
Title: The appell hypergeometric functions and classical separable mechanical systems
Journal: Journal of Physics A: Mathematical and General
Volume: 35
Issue: 9
First page: 2213
Last page: 2221
Issue Date: 8-Mar-2002
Rank: M21
ISSN: 0305-4470
DOI: 10.1088/0305-4470/35/9/311
Abstract: 
A relationship between two old mathematical subjects is observed: the theory of hypergeometric functions and the separability in classical mechanics. Separable potential perturbations of integrable billiard systems and the Jacobi problem for geodesies 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 increase. Wider classes of separable potentials are given by the obtained new formulae automatically.
Publisher: IOP Science

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