Formulas for the Fourier Series of Orthogonal Polynomials in Terms of Special Functions
نویسنده
چکیده
An explicit formula for the Fourier coef cients of the Legendre polynomials can be found in the Bateman Manuscript Project. However, 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. The methods described here apply in principle to an class of polynomials, including non-orthogonal polynomials. Index TermsFourier series, Gegenbauer polynomials, Jacobi polynomials, Laguerre polynomials, Hermite polynomials. An explicit formula for the Fourier coef cients of Legendre polynomials appears in the Bateman Manuscript Project [3, 4, 5, 6]. One nds that Pn(x) = 1 X k= 1 b Pn (k) e x (1) where b Pn (k) = 1 2 Z 1
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