Fourier series of orthogonal polynomials

Authors:
Nataniel Greene
Affiliations:
Department of Mathematics and Computer Science, Kingsborough Community College, CUNY, Brooklyn, NY
Venue:
MATH'08 Proceedings of the American Conference on Applied Mathematics
Year:
2008

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Abstract

Explicit formulas for the Fourier coeffcients of the Legendre polynomials can be found in the Bateman Manuscript Project. However, similar formulas for more general classes of orthogonal polynomials do not appear to have been worked out. Here we derive explicit formulas for the Fourier series of Gegenbauer, Jacobi, Laguerre and Hermite polynomials.