Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

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

Published

Author(s)

Roberto S. Costas-Santos, Howard Cohl

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

Keywords

Ferrers functions, Gegenbauer polynomials, orthogonal polynomials

Citation

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 19, 2024)
Created March 30, 2022, Updated March 27, 2024