Abstract
The internal potential of a homogeneous circular torus first is represented by a series expansion in spherical functions (Laplace series). Exact analytical formulas for the coefficients of this series are derived and it is shown that they can be expressed through the standard Gauss hypergeometric function depending only on the geometric parameter of the torus. Convergence of the series is proved and the radius of convergence is determined. The relation of the radius with the torus geometrical parameter is found. A special spherical shell, where the problem of expansion of the torus potential should be solved in additional investigations, is detected.
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B. P. Kondratyev, A. S. Dubrovskii, N. G. Trubitsyna, and E. Sh. Mukhametshina, Zh. Tekh. Fiz. 79(2), 17 (2009) [Tech. Phys. 54, 176 (2009)].
B. P. Kondratyev, Theory of Potential and Equilibrium Figures (RKhD, Moscow-Izhevsk, 2003) [in Russian].
B. P. Kondratyev, Theory of Potential: New Methods and Problems with Solutions (Mir, Moscow, 2007).
V. A. Antonov, E. I. Timoshkova, and K. V. Kholshevnikov, An Introduction to the Theory of Newtonian Potential (Nauka, Moscow, 1988) [in Russian].
M. Abramovitz and I. A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1971; Nauka, Moscow, 1979).
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Published in Russian in Zhurnal Tekhnicheskoĭ Fiziki, 2010, Vol. 80, No. 1, pp. 23–26.
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Kondratyev, B.P., Trubitsina, N.G. Laplace series expansion of the internal potential of a homogeneous circular torus. Tech. Phys. 55, 22–25 (2010). https://doi.org/10.1134/S1063784210010044
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DOI: https://doi.org/10.1134/S1063784210010044