@article{ajma2021912,
author={Parfenov, Michael},
title={On Constructing Complicated Compositions of Quaternionic Holomorphic Functions},
journal={American Journal of Mathematical Analysis},
volume={9},
number={1},
pages={6--26},
year={2021},
url={http://pubs.sciepub.com/ajma/9/1/2},
issn={2333-8431},
abstract={The issue of constructing complicated quaternionic holomorphic (<img src=image/abs1.png></img>-holomorphic) functions in the Cayley-Dickson doubling form is considered. The way of <img src=image/abs2.png></img><i>-</i>holomorphic substitutions, allowing us to construct <img src=image/abs3.png></img><i>-</i>holomorphic composite functions of any degree of difficulty, is presented. The new <img src=image/abs4.png></img>¨Crepresentation form for <img src=image/abs5.png></img><i>-</i>holomorphic functions is established as a consequence of the earlier proved commutative behavior of the quaternionic multiplication in the case of <img src=image/abs6.png></img><i>-</i>holomor¨¹hic functions. The specific polar form of <img src=image/abs7.png></img><i>-</i>holomorphic functions with a real-valued modulus and argument similar to complex one is obtained. The <img src=image/abs8.png></img><i>-</i>holomorphic generalizations of the logarithmic and inverse trigonometric and hyperbolic functions are implemented. The obtained results reaffirm that any complicated <img src=image/abs9.png></img><i>-</i>holomorphic function can be constructed from its complex holomorphic analog. The processing of <img src=image/abs10.png></img><i>-</i>holomorphic functions of any degree of difficulty is provided through high-speed programmes in system Wolfram Mathematica<SUP>?</SUP> represented in the Appendix.},
doi={10.12691/ajma-9-1-2}
publisher={Science and Education Publishing}
}