A new and efficient method for the computation of Legendre coefficients

2011/06/02 by Enrico De Micheli, De Micheli, Enrico, G. A. Viano +1 · 2 citations
Computer Science · #42C10 #65T50 #Digital Filter Design and Implementation #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical Analysis (math.NA) #Numerical Methods and Algorithms #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1106.0463

openalex publication_date 2011/06/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

An efficient procedure for the computation of the coefficients of Legendre expansions is here presented. We prove that the Legendre coefficients associated with a function f(x) can be represented as the Fourier coefficients of an Abel-type transform of f(x). The computation of N Legendre coefficients can then be performed in O(N log N) operations with a single Fast Fourier Transform of the Abel-type transform of f(x).

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• The expansion in ultraspherical polynomials: a simple procedure for the fast computation of the ultraspherical coefficients
• Fast and highly accurate computation of Chebyshev expansion coefficients of analytic functions

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