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