On the Laplace equation in d-dimension
R. R. Landim
TL;DR
This paper introduces a method to derive the general solution of the Laplace equation in any number of dimensions using ultraspherical coordinates, expanding analytical tools for high-dimensional potential problems.
Contribution
The paper presents a novel approach to solve the Laplace equation in arbitrary dimensions utilizing ultraspherical coordinates, which was not previously established.
Findings
Derived the general solution in d-dimensions
Extended potential theory to higher dimensions
Provided analytical expressions for solutions
Abstract
We develop a method to obtain the general solution of the Laplace equation in -dimension in ultraspherical coordinates.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Electromagnetic Scattering and Analysis · Algebraic and Geometric Analysis