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The growth of an entire harmonic function in \(\mathbb{R}^ 3\). (English) Zbl 0878.30023

Summary: A function which is harmonic in a neighbourhood of the origin in \(\mathbb{R}^2\) has there an expansion in spherical harmonics. The authors have defined generalized \((p,q)\)-type and generalized lower \((p,q)\)-type of an entire harmonic function in \(\mathbb{R}^3\) with respect to proximate order and obtain coefficient characterizations for these growth parameters.

MSC:

30D15 Special classes of entire functions of one complex variable and growth estimates
30B20 Random power series in one complex variable
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