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.
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Communicated by Irene Sabadini.
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Cervantes, J.O.G., Cordero, J.E.P. & Campos, D.G. On Some Quaternionic Series. Adv. Appl. Clifford Algebras 33, 45 (2023). https://doi.org/10.1007/s00006-023-01293-9
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DOI: https://doi.org/10.1007/s00006-023-01293-9