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arXiv · 2407.21474

On Decompositions of H-holomorphic functions into quaternionic power series

Michael Parfenov
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Abstract

Based on the full similarity in algebraic properties and differentiation rules between quaternionic (H-) holomorphic and complex (C-) holomorphic functions, we assume that there exists one holistic notion of a holomorphic function that has a H-representation in the case of quaternions and a C-representation in the case of complex variables. We get the essential definitions and criteria for a quaternionic power series convergence, adapting complex analogues to the quaternion case. It is established that the power series expansions of any holomorphic function in C- and H-representations are similar and converge with identical convergence radiuses. We define a H-analytic function and prove that every H-holomorphic function is H-analytic. Some examples of power series expansions are given.

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Michael Parfenov. 2024-07-31. On Decompositions of H-holomorphic functions into quaternionic power series. https://arxiv.org/abs/2407.21474

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