On the solution of the partial differential equation i=1N(2+ki2)=0

It is shown that the solution of the partial differential equation i=1N(2+ki2) = 0, (ki2 kj2) subject to appropriate boundary conditions may be written as = i=1Nii where the i's are the solutions of the Helmholtz equation (2 + ki2)i = 0 and the i's are constants. The explicit forms of the i's in terms of the boundary values are also given. It is also shown that the solution of the partial differential equation (2 + k2)N = 0 is obtained by means of a certain limiting procedure from the solution of the nondegenerate problem. Copyright 1973 by the American Institute of Physics.

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