Geodesic
On the derivatives at the origin of entire harmonic functions
Glasgow mathematical journal, Tome 20 (1979) no. 2, pp. 147-154

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If f is an entire function in the complex plane such thatwhere 0 ≤ α < 1, and all the derivatives of f at 0 are integers, then it is easy to show that f is a polynomial (see e.g. Straus [10]). The best possible result of this type was proved by Pólya [9]. The main aim of this paper is to prove two analogous results for harmonic functions defined in the whole of the Euclidean space Rn, where n ≥ 2 (i.e. entire harmonic functions). 
Armitage, D. H. On the derivatives at the origin of entire harmonic functions. Glasgow mathematical journal, Tome 20 (1979) no. 2, pp. 147-154. doi: 10.1017/S0017089500003864
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