中文摘要：

给出了k -超正则函数的开拓定理和唯一性定理，由唯一性定理证明了超正则函数列的内闭一致收敛性; 由k -超正则函数的P 部和Q 部满足的两个微分方程，讨论了此方程与k -超正则函数及其相关函数的关系.

英文摘要：

In the first part of this paper, the authors show the extension theorem and uniqueness theorem of k-hypermonogenic functions. What is more, by the uniqueness theorem, the authors prove the inner-closed uniform convergence of sequence of hypermonogenic functions. In the second part of this paper, as P-part and Q-part of k-hypermonongenic functions satisfy two equations, the authors discuss the relationship between these two equations and k- hypermonogenic functions and their relative functions.