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MIXED SECOND-ORDER QUATERNIONIC DERIVATIVES: ADVANCES ON HYPERCOMPLEX
Keywords:
quaternionic derivative, hypercomplex analysis, derivativeDOI:
https://doi.org/10.17654/0972087126030Abstract
Over the past decades, the study of quaternions has advanced significantly, primarily in the field of mathematical analysis [1-5]. These advances have brought to light various generalizations of the Classical Theory of Complex Analysis, especially in the differentiation and integration of quaternionic functions. In the realm of quaternionic differentiation, new methods have been developed to handle the peculiarities of quaternionic functions, highlighting the Cauchy-Riemann Equations and a “closed” formulation for the Cauchy Integral [6, 7]. The main objective of this article is to demonstrate the equality of the mixed second quaternionic derivatives. This equality is fundamental for the theoretical development of quaternionic analysis and can provide new perspectives and applications related fields.
Received: September 27, 2025
Accepted: October 29, 2025
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