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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.21474 |
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| _version_ | 1866910548519550976 |
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| author | Parfenov, Michael |
| author_facet | Parfenov, Michael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21474 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Decompositions of H-holomorphic functions into quaternionic power series Parfenov, Michael Complex Variables 30G35 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. |
| title | On Decompositions of H-holomorphic functions into quaternionic power series |
| topic | Complex Variables 30G35 |
| url | https://arxiv.org/abs/2407.21474 |