Geodesic
Series Expansions of Generalized Temperature Functions in N Dimensions
Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 794-802

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The generalized heat equation is given by 1.1 where Δxf(x) = f′′(x) + (2v/x)f′(x), v a fixed positive number. In a recent paper (5), the author established criteria for representing solutions of (1.1) in either the form 1.2 or 1.3 where Pn,v(x, t) is t he polynomial solution of (1.1) given explicitly by 1.4 and Wn,v(x, t) is its Appell transform; cf. (1). Our object is to generalize these results by extending them to higher dimensions. D. V. Widder (8) studied the problem for the ordinary heat equation. 
Haimo, Deborah Tepper. Series Expansions of Generalized Temperature Functions in N Dimensions. Canadian journal of mathematics, Tome 18 (1966) no. 1, pp. 794-802. doi: 10.4153/CJM-1966-078-0
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