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

SPRINGER (HUNGARY) | ISSN: 0133-3852 | JCR┬« 2021 Impact Factor: 0.703 - MATHEMATICS — position: 241/332 (Q3/T3)  
title

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

Cohl, H. S., Costas-Santos, R. S. Analysis Mathematica 48, no. 3 (2022), 695--716

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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BibTeX

@article {MR4467827,
AUTHOR={Cohl, H. S. and Costas-Santos, R. S.},
TITLE={On the relation between {G}egenbauer polynomials and the {F}errers function of the first kind},
JOURNAL={Anal. Math.},
FJOURNAL={Analysis Mathematica},
VOLUME={48},
YEAR={2022},
NUMBER={3},
PAGES={695--716},
ISSN={0133-3852},
MRCLASS={33C05 (33C45 42C05 42C10 44A20)},
MRNUMBER={4467827},
DOI={10.1007/s10476-022-0123-0},
URL={https://doi.org/10.1007/s10476-022-0123-0},
}