Costas-Santos, R.
and Cohl, H.
(2022),
On the relation between Gegenbauer polynomials and the Ferrers function of the first kind, Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), [online], https://doi.org/10.1007/s10476-022-0123-0, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=932710
(Accessed April 27, 2024)
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On the relation between Gegenbauer polynomials and the Ferrers function of the first kind
Published
Author(s)
Roberto S. Costas-Santos,
Abstract
Using the direct relation between the Gegenbauer polynomials C_n^λ(x) and the Ferrers function of the first kind P_μ^ν(x), we compute interrelations between certain Jacobi polynomials, Meixner polynomials, and Ferrers functions of the first and second kind. We then compute Rodrigues-type, standard integral orthogonality and Sobolev orthogonality relations for Ferrers functions of the first and second kinds. In the remainder of the paper using the relation between Gegenbauer polynomials and the Ferrers function of the first kind we derive connection and linearization relations, some definite integral and series expansions, Christoffel–Darboux summation formulas, Poisson kernel and infinite series closure relations (Dirac delta distribution expansions).Citation
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume
48
Issue
3
Pub Type
Journals
Download Paper
Keywords
Ferrers functions, Gegenbauer polynomials, orthogonal polynomials
Citation
Created March 30, 2022, Updated March 27, 2024