中文摘要：

在实k-超正则向量值函数和实k-超调和向量值函数定义的基础上,首先给出了复k-超正则向量值函数和复k-超调和向量值函数的定义,然后引入了一个偏微分方程组,借助这个偏微分方程组讨论了复k-超正则向量值函数的性质及其与复k-超调和向量值函数的关系,最后得到这个偏微分方程组可解性的充分必要条件.

英文摘要：

In this paper,on the basis of the definition of the k-hypermonogenic and khyperbolically harmonic functions with vector value in real Clifford analysis,the definition of the k-hypermonogenic functions and k- hyperboUcally harmonic functions with vector value in complex Clifford analysis is given.Then,some properties of complex k-hypermonogenic and k- hyperbolically harmonic functions with vector value and their relation are discussed by introducing a partial differential equation system.Furthermore,a necessary and sufficient condition for the solvability of the partial differential equation system is obtained.