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.

本文讨论广义轴对称势（GASP），它是\（\ 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，\\\ mathbb {N}。\） GASP已被几代数学家研究。在本文中，我们通过Clifford分析设置中的谐波函数，通过微分算子引入GASP的显式表示。