全空间上Hypergenic函数的积分表示

Integral Representations for Hypergenic Functions in the Whole Space

本文首先借助hypergenic函数改进的柯西积分公式,呈现了hypergenic函数改进的柯西积分公式的另一种形式。接着,基于hypergenic函数与对偶的hypergenic函数两者之间的关系,我们推导出了对偶的hypergenic函数所对应的改进的柯西型积分公式。最后,进一步探讨并推导了关于(1 − n)-hypergenic函数的改进的积分表示。In this article, with the help of the hypergenic function for the improved Cauchy integral formula, we first give another form of the hypergenic function for the improved Cauchy integral formula. Then, on the basis of the relationship between hypergenic function and the dual hypergenic function, the dual hypergenic function for the improved Cauchy integral formula is obtained. Finally, the related results of a (1 − n)-hypergenic function for the improved integral representation are derived.