Solution of Three-Dimensional Problems for the Hyperboloid of Revolution and the Lens in Electrical Prospecting

Part of the Seminars in Mathematics book series (SM, volume 9)


In this paper solutions are given for problems of the potential distribution created by a point source of current in the case of a hyperbolic or spherical boundary of separation. The solutions are obtained by integrating the Laplace equation in degenerate ellipsoidal (toroidal) coordinates. To find the coefficients, a generalization of the Mehler-Fok integral theorem to the case m≠Q ft is used. The final expressions for the potential functions are given in the form of series whose coefficients are given by real integrals.


Point Source Potential Function Half Space Potential Distribution Laplace Equation 
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Literature Cited

  1. 1.
    Lebedev, N. N., Special Functions and Their Applications [in Russian] (1953).Google Scholar
  2. 2.
    Nikolaev, B. G., The expansion of an arbitrary function in terms of an integral of associated Legendre functions of first kind with complex index, this volume, p. 45,Google Scholar
  3. 3.
    Glyuzman, A. M., Solution of the boundary value problem for the hyperboloid of revolution in electrical prospecting, Izv. Akad. Nauk SSSR, No. 5 (1961).Google Scholar

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© Consultants Bureau, New York 1970

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