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首页> 外文期刊>American Journal of Mathematical Analysis >On Properties of Holomorphic Functions in Quaternionic Analysis
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On Properties of Holomorphic Functions in Quaternionic Analysis

机译:四元数分析中全纯函数的性质

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We draw the conclusions from the earlier presented quaternionic generalization of Cauchy-Riemann’s equations. The general expressions for constituents of -holomorphic functions as well as the relations between them are deduced. The symmetry properties of constituents of -holomorphic functions and their derivatives of all orders are proved. For full derivatives it is a consequence of uniting the left and right derivatives within the framework of the developed theory. Some -holomorphic generalizations of ?- holomorphic functions are discussed in detail to demonstrate particularities of constructing H-holomorphic functions. The power functions are considered in detail.
机译:我们从早先提出的Cauchy-Riemann方程的四元数泛化中得出结论。推导了-全纯函数的组成部分的一般表达式以及它们之间的关系。证明了-全纯函数的组成部分及其所有阶的导数的对称性质。对于全导数,这是在发达理论的框架内将左右导数结合在一起的结果。详细讨论了β-全纯函数的一些-全纯泛化,以证明构造H-全纯函数的特殊性。功率功能被详细考虑。

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