As an integral representation for holomorphic functions, Cauchy integral formula plays a significant role in the function theory of one complex variable and several complex variables. In this paper, using the idea of several complex analysis we construct the Cauchy kernel in universal Clifford analysis, which has generalized complex differential forms with universal Clifford basic vectors. We establish Cauchy–Pompeiu formula and Cauchy integral formula on the distinguished boundary with values in universal Clifford algebra. This work is the basis for studying the Cauchy-type integral and its boundary value problem in complex universal Clifford analysis.

作为全纯函数的积分表示，柯西积分公式在一个复变量和多个复变量的函数论中占有重要地位。在本文中，我们利用几种复分析的思想构造了通用 Clifford 分析中的 Cauchy 核，它用通用 Clifford 基本向量推广了复微分形式。我们在通用 Clifford 代数中的值的区分边界上建立了柯西-庞贝公式和柯西积分公式。这项工作是研究复杂通用 Clifford 分析中柯西型积分及其边值问题的基础。