Peanut harmonic expansion for a fundamental solution of Laplace's equation in flat-ring coordinates

DOI10.1007/s10476-022-0175-1OpenAlexW4296023035WikidataQ114227586 ScholiaQ114227586MaRDI QIDQ2678403

Lijuan Bi, Howard S. Cohl, Hans W. Volkmer

Publication date: 23 January 2023

Published in: Analysis Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2202.08923

zbMATH Keywords

orthogonal polynomialsfundamental solutionspecial functionsLaplace's equationflat-ring cyclide coordinatesseparable curvilinear coordinate system

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Other special orthogonal polynomials and functions (33C47) Classical hypergeometric functions, ({}_2F_1) (33C05) Spherical harmonics (33C55) Elliptic integrals as hypergeometric functions (33C75)

Related Items

Internal and external harmonics in bi-cyclide coordinates

Uses Software

• DLMF

Cites Work

• Eigenvalue problems for Lamé's differential equation
• Expansion for a fundamental solution of Laplace's equation in flat-ring cyclide coordinates
• Developments in determining the gravitational potential using toroidal functions
• Integral Representations for Products of Lamé Functions by Use of Fundamental Solutions
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