A generalized monogenic exponential function in ℍ. Issue 11 (2nd November 2019)

• Record Type: Journal Article
• Authors: Bock, Sebastian
• Is Part Of: Complex variables and elliptic equations. Volume 64:Issue 11(2019)
• Page Start: 1881
• Page End: 1897
• Publication Date: 2019-11-02
• Subjects: Quaternionic analysis -- generalized exponential function -- Appell polynomial -- generalized Taylor series; 30G35 -- 33B10; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2019.1565407
• Languages: English
• ISSNs: 1747-6933

Abstract

ABSTRACT: The article presents a monogenic exponential function for the hypercomplex function theory of quaternion-valued monogenic functions in a reduced quaternionic variable, which has essential properties analogous to the complex exponential function e z, z ∈ C . In particular, it is shown that the Taylor series of the monogenic exponential function based on a complete orthogonal system of monogenic Appell polynomials also generalizes the corresponding complex series representation in a canonical manner.