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Paper: On the relation between Gegenbauer polynomials and the Ferrers function of the first kind


On the relation between Gegenbauer polynomials and the Ferrers function of the first kind

Howard S Cohl, Roberto S. Costas-Santos — Analysis Mathematica — Accepted in 2021

SPRINGER (HUNGARY) | ISSN: 0133-3852 | JCR┬« 2020 Impact Factor: 0.788 - MATHEMATICS — position: 217/330 (Q2/T2)

Abstract

Using the direct relation between the Gegenbauer polynomials and the Ferrers function of the first kind, 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).

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