New solutions of the generalized ellipsoidal wave equation

  • Harold Exton
Keywords: Ellipsoidal, Heun, Hypergeometric


Certain aspects and a contribution to the theory of new forms of solutions of an algebraic form of the generalized ellipsoidal wave equation are deduced by considering the Laplace transform of a soluble system of linear differential equations. An ensuing system of non-linear algebraic equations is shown to be consistent and is numerically implemented by means of the computer algebra package MAPLE V. The main results are presented as series of hypergeometric type of there and four variables which readily lend themselves to numerical handling although this does not indicate all of the detailed
analytic properties of the solutions under consideration.