This article provides a closed form solution to the telegrapherâ??s equation with\nthree space variables defined on a subset of a sphere within two radii, two\nazimuthal angles and one polar angle. The Dirichlet problem for general\nboundary conditions is solved in detail, on the basis of which Neumann and\nRobin conditions are easily handled. The solution to the simpler problem in\ncylindrical coordinates is also provided. Ways to efficiently implement the\nformulae are explained. Minor adjustments result in solutions to the wave\nequation and to the heat equation on the same domain as well, since the latter\nare particular cases of the more general telegrapherâ??s equation.
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