Fundamental solutions and Gegenbauer expansions of Helmholtz operators in Riemannian spaces of constant curvature

DOI10.3842/SIGMA.2018.136zbMath1406.35106arXiv1803.07149OpenAlexW2789294606WikidataQ128676243 ScholiaQ128676243MaRDI QIDQ1755889

Thinh H. Dang, T. M. Dunster, Howard S. Cohl

Publication date: 11 January 2019

Published in: SIGMA. Symmetry, Integrability and Geometry: Methods and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1803.07149

zbMATH Keywords

fundamental solutionHelmholtz equationhyperbolic geometryGegenbauer serieshyperspherical geometryFerrers functions

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Elliptic equations on manifolds, general theory (58J05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (6)

Explicit Expressions of the Hua--Pickrell Semigroup ⋮ Mehler–Fock transforms and retarded radiative Green functions in hyperbolic and spherical spaces ⋮ Analytic structure of the associated Legendre functions of the second kind ⋮ Uniform asymptotic expansion of Legendre functions ⋮ Large-Parameter Asymptotic Expansions for the Legendre and Allied Functions ⋮ Gegenbauer expansions and addition theorems for a binomial and logarithmic fundamental solution of the even-dimensional Euclidean polyharmonic equation

Uses Software

• DLMF

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