New methods in the theory of the Newtonian potential. II - The potential energy of homogeneous lense-shaped bodies and spherical segments

Mathematics

Scientific paper

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Functions (Mathematics), Gravitational Lenses, Newton Theory, Potential Theory, Series (Mathematics), Integral Equations, Spheres

Scientific paper

The method of representing the potential energy of homogeneous gravitating, as well as electrically charged, bodies in the form of special series is used to find the energy of a spherical segment segmented of symmetrical and asymmetrical lenses. Expressions for the energy of these bodies in closed analytical form are obtained and represented through elementary functions from parameters of the geometrical form of the configuration. A summation of the above series is performed on the basis of the complex variable function theory.

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