A generalized monogenic exponential function in ℍ

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 ${\mathit{e}}^{\mathit{z}}$, $\mathit{z}\in \mathbb{C}$. 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.

KEYWORDS:

• Quaternionic analysis
• generalized exponential function
• Appell polynomial
• generalized Taylor series

AMS SUBJECT CLASSIFICATIONS:

• 30G35
• 33B10

Disclosure statement

No potential conflict of interest was reported by the author.

ORCID

Sebastian Bock http://orcid.org/0000-0002-0660-6156