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On the Solution of a Weinstein-Type Equation in \(\mathbb {R}^3\)

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Abstract

This paper deals with generalized axially symmetric potentials (GASP) which are solutions of a Weinstein-type equation in \(\mathbb {R}^3\) \(\dfrac{\partial ^2\Phi }{\partial x^2}+\dfrac{\partial ^2\Phi }{\partial y^2}+\dfrac{\partial ^2\Phi }{\partial z^2}+\dfrac{2(m+1)}{z}\dfrac{\partial \Phi }{\partial z}=0,\ m\in \mathbb {N}.\) GASP have been investigated by several generations of mathematicians. In this paper, we introduce an explicit representation of the GASP by differential operators via harmonic functions in Clifford analysis setting.

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Acknowledgements

The author would like to express his sincere gratitude to the Anonymous Reviewers for their very important comments to improve this paper.

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  1. School of Applied Mathematics and Informatics, Hanoi University of Science and Technology, Hanoi, Vietnam

    Doan Cong Dinh

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  1. Doan Cong Dinh
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Correspondence to Doan Cong Dinh.

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Communicated by Swanhild Bernstein

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Dinh, D.C. On the Solution of a Weinstein-Type Equation in \(\mathbb {R}^3\). Adv. Appl. Clifford Algebras 31, 7 (2021). https://doi.org/10.1007/s00006-020-01110-7

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