Year: 2026
Type: article
Abstract: We describe the solutions to a family of rotationally symmetric second order partial differential equations in the complex plane that arises from a four-dimensional complex Lie algebra whose spanning set generates the algebra from which such generalised harmonic functions derive. We show that every one of these solutions have a canonical series representation and retrieve those obtained in the case of Laplace and Helmholtz equation. These sums are given in confluent hypergeometric terms that asymptotically correspond to the complex exponential function.
Source: The Journal of Analysis
Author: Markus Klintborg
Institutions: Lund University, University of Borås
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,090
Funder: Vetenskapsrådet
OpenAlex ID: W7155010874