由二維拉普拉斯方程式之精確解實例出發，本文探討不同區域Poisson核之摺積公式。透過複變分析中的留數定理，可以直接證明這些數學等式。最後，我透過複平面保角變換，聯繫不同區域之Poisson核及其摺積公式。

Based on examples of the exact solutions of the two-dimensional Laplace's equation, I derive the convolution formulas among the Poisson kernels associated with given domains. These mathematical identities can be verified directly using the residue theorem in the complex analysis. The interconnections of convolution formulas for different domains are established via a conformal transformation.