Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2022
• Main Authors: Bi, Lijuan, Cohl, Howard S., Volkmer, Hans
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2022
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211627
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Expansion for a Fundamental Solution of Laplace's Equation in Flat-Ring Cyclide Coordinates. Lijuan Bi, Howard S. Cohl and Hans Volkmer. SIGMA 18 (2022), 041, 31 pages

We derive an expansion for the fundamental solution of Laplace's equation in flat-ring coordinates in three-dimensional Euclidean space. This expansion is a double series of products of functions that are harmonic in the interior and exterior of ''flat rings''. These interna...