On Some Quaternionic Series

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-07-31 DOI:10.1007/s00006-023-01293-9

J. Oscar González Cervantes, J. Emilio Paz Cordero, Daniel González Campos

引用次数: 0

Abstract

The aim of this work is to show that given \(u\in {\mathbb {H}}{\setminus }{\mathbb {R}}\), there exists a differential operator \(G^{-u}\) whose solutions expand in quaternionic power series expansion \( \sum _{n=0}^\infty (x-u)^n a_n\) in a neighborhood of \(u\in {\mathbb {H}}\). This paper also presents Stokes and Borel-Pompeiu formulas induced by \(G^{-u}\) and as consequence we give some versions of Cauchy’s Theorem and Cauchy’s Formula associated to these kind of regular functions.

查看原文本刊更多论文

关于一些四元数级数

这项工作的目的是证明给定\（u\ in｛\mathbb｛H｝｝｛\setminus｝｛\mathbb{R｝），存在一个微分算子\（G^｛-u｝\），其解在\（u\in｛\ mathbb｛H}｝）的邻域中以四元幂级数展开\（\sum_｛n=0｝^\infty（x-u）^n a_n\）展开。本文还给出了由\（G^｛-u｝）导出的Stokes和Borel Pompeiu公式，并由此给出了与这类正则函数相关的Cauchy定理和Cauchy公式的一些版本。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.