Mutually inverse series relating Ferrers and associated Legendre functions and generating functions pertaining to them

DOI10.1016/j.jmaa.2023.127575arXiv2306.05158MaRDI QIDQ6050958

Pinchas Malits

Publication date: 19 September 2023

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2306.05158

zbMATH Keywords

generating functionsGegenbauer polynomialshypergeometric polynomialsassociated Legendre functionsFerrers functionsassociated Legendre polynomials

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Inverse theorems in approximation theory (41A27)

Cites Work

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• Spherical harmonics and approximations on the unit sphere. An introduction
• Associated Legendre functions and spherical harmonics of fractional degree and order
• On the relation between Gegenbauer polynomials and the Ferrers function of the first kind
• Completely integrable relativistic Hamiltonian systems and separation of variables in Hermitian hyperbolic spaces
• Gegenbauer Approximation in Certain Hilbert Spaces and Its Applications to Singular Differential Equations
• Legendre functions of fractional degree: transformations and evaluations
• The Polynomial of Mittag-Leffler

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