Associated Legendre functions and spherical harmonics of fractional degree and order

DOI10.1007/s00365-017-9403-5zbMath1404.33008arXiv1702.08555OpenAlexW2594295338WikidataQ59615702 ScholiaQ59615702MaRDI QIDQ1615924

Robert S. Maier

Publication date: 31 October 2018

Published in: Constructive Approximation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.08555

zbMATH Keywords

spherical harmonicJacobi polynomialalgebraic functionassociated Legendre functionladder operatorHeun polynomialsolid harmonic

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Applications of Lie groups to the sciences; explicit representations (22E70) Other special orthogonal polynomials and functions (33C47) Spherical harmonics (33C55)

Related Items (4)

Mutually inverse series relating Ferrers and associated Legendre functions and generating functions pertaining to them ⋮ Explicit general solution of the squared secant potential and some consequences ⋮ A bi-directional method for evaluating integrals involving higher transcendental functions. HyperRAF: a Julia package for new hyper-radial functions ⋮ Fundamental solutions for the Laplace-Beltrami operator defined by the conformal hyperbolic metric and Jacobi polynomials

Uses Software

• DLMF

Cites Work

• Factorization method in quantum mechanics
• Algebraic special functions and \(\mathrm{SO}(3,2)\)
• Master analytic representations and unified representation theory of certain orthogonal and pseudo-orthogonal groups
• DIHEDRAL GAUSS HYPERGEOMETRIC FUNCTIONS
• Expansions in Series of Legendre Functions
• The representation of the S O (4,1) group in four−dimensional Euclidean and spinor space
• Finite Sum Evaluation of the Gauss Hypergeometric Function in an Important Special Case
• Abel Summability of Certain Series of Legendre Functions
• POLYNOMIALS ASSOCIATED WITH THE HYPERGEOMETRIC FUNCTIONS WITH FINITE MONODROMY GROUPS
• Fractional operators and special functions. II. Legendre functions
• Legendre functions of fractional degree: transformations and evaluations
• Discrete Series for the Universal Covering Group of the 3 + 2 de Sitter Group
• Représentations intégrables du groupe de De Sitter
• Matrix Elements for the Most Degenerate Continuous Principal Series of Representations of SO(p, 1)
• Symmetries of Differential Equations. The Hypergeometric and Euler–Darboux Equations
• Lie Theory and Generalizations of the Hypergeometric Functions
• EXPRESSIONS FOR VALUES OF THE GAMMA FUNCTION
• An Essay Toward a Unified Theory of Special Functions. (AM-18)
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Associated Legendre functions and spherical harmonics of fractional degree and order