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with A M = ^ + [ ( M ~ l)/r]Dr. Results have been obtained when <f>(r) is entire of growth (1, a) in r [ l ] , [3], [4] and these have been extended to the L2 theory in [3]. In this note, we state some results on the structures of solutions of (1) when the data function <£(r) has a pole a t r = 0 but is otherwise entire. These structures are defined in terms of convolution integrals and the proofs are based on the Laplace transform formulation [2] of solutions of (1) and the expansion theory referred to above. The details of the proofs will appear in a forthcoming paper that will also discuss logarithmic singularities. We denote by ?>(r, t; <!>(/)) the solution of (1) defined by

The radial heat equation with pole type data