ABSTRACT
This technique was applied by many authors for the case of impulse source (Morse and Ingard, 1968), when this series is convergent, since only a nite number of virtual sources can contribute to the response at a certain moment. We can apply this approach to the harmonic process, which leads, in the 2D case, to the following result:
p(x1, y1) = s(x0 – x1, y0 – y1, a, b) + s(x0 + x1, y0 – y1, a, b) + s(x0 – x1, y0 + y1, a, b) + s(x0 + x1, y0 + y1, a, b), (4.101)
where the function S is given by the double series
s(x, y, a, b) = ∞∑
[ k √
(x + 2am)2 + (y + 2bn)2 ]. (4.102) Although the solution is expressed in explicit form (4.102), the series does not converge in any classical sense (see Section 1.3). Thus, we cannot use divergent series (4.102) for direct computations.
