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Technical Physics

, Volume 54, Issue 2, pp 176–181 | Cite as

Laplace series expansion of the potential of a homogeneous circular torus

  • B. P. Kondrat’ev
  • A. S. Dubrovskii
  • N. G. Trubitsyna
  • É. Sh. Mukhametshina
Theoretical and Mathematical Physics

Abstract

The external potential of a homogeneous circular torus is represented by a series expansion in spherical functions (Laplace series). Exact analytical formulas are derived for the coefficients of this series, which can be expressed in terms of Legendre polynomials depending only on the geometrical parameter of the torus. The convergence of the series is proved and the radius of convergence is determined. The resultant expressions are verified numerically.

PACS numbers

92.30.Em 

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References

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Copyright information

© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  • B. P. Kondrat’ev
    • 1
  • A. S. Dubrovskii
    • 1
  • N. G. Trubitsyna
    • 1
  • É. Sh. Mukhametshina
    • 1
  1. 1.Udmurtia State UniversityIzhevskRussia

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