In the first part of this paper, as P-part and Q-part of k-hypermongenic functions are satisfied with two equations, we discuss the relationship between these two equations and k-hypermongenic functions and their relative functions. In the second part of this paper, we show the k-hypermongenic prolongation theorem and the k-hypermongenic uniqueness theorem. What is more, by the k-hypermongenic uniqueness theorem, we prove the convergence of squence with k-hypermongenic function terms. |