Authors:
Michael Parfenov
Pages: 6 - 26 Abstract: The issue of constructing complicated quaternionic holomorphic (-holomorphic) functions in the Cayley-Dickson doubling form is considered. The way of -holomorphic substitutions, allowing us to construct -holomorphic composite functions of any degree of difficulty, is presented. The new –representation form for -holomorphic functions is established as a consequence of the earlier proved commutative behavior of the quaternionic multiplication in the case of -holomorühic functions. The specific polar form of -holomorphic functions with a real-valued modulus and argument similar to complex one is obtained. The -holomorphic generalizations of the logarithmic and inverse trigonometric and hyperbolic functions are implemented. The obtained results reaffirm that any complicated -holomorphic function can be constructed from its complex holomorphic analog. The processing of -holomorphic functions of any degree of difficulty is provided through high-speed programmes in system Wolfram Mathematica® represented in the Appendix. PubDate: 2022-01-04 DOI: 10.12691/ajma-9-1-2 Issue No:Vol. 9, No. 1 (2022)

Authors:
Theophilus Agama
Pages: 1 - 5 Abstract: The goal of this paper is to prove the identity where and where is the Gamma function defined by and is the Euler-Mascheroni constant. PubDate: 2021-02-23 DOI: 10.12691/ajma-9-1-1 Issue No:Vol. 9, No. 1 (2021)