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In this paper certain Bessel type eigenfunction expansions are developed by considering a non-seif-adjoint problem which involves a radiation type condition

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1. There has been considerable debate on the conditions under which a given function f(r) can be expanded as a series of the orthogonal functions where υ1, υ2, … are the zeros of the Hankel function regarded as a function of its order. Here k, a are positive constants and 0 < a ≤ r < ∞. The formal expansion can be written aswhere