The Fourier Transforms of the Chebyshev and Legendre Polynomials

The Fourier Transforms of the Chebyshev and Legendre Polynomials

Analytic expressions for the Fourier transforms of the Chebyshev and Legendre polynomials are derived, and the latter is used to find a new representation for the half-order Bessel functions. The numerical implementation of the so-called unified method in the interior of a convex polygon provides an...

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Veröffentlicht in:arXiv.org 2012-11
Hauptverfasser: Fokas, A S, Smitheman, S A
Format: Artikel
Sprache:eng
Schlagworte:
Bessel functions
Chebyshev approximation
Exact solutions
Fourier transforms
Mathematical analysis
Polynomials
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Zusammenfassung:Analytic expressions for the Fourier transforms of the Chebyshev and Legendre polynomials are derived, and the latter is used to find a new representation for the half-order Bessel functions. The numerical implementation of the so-called unified method in the interior of a convex polygon provides an example of the applicability of these analytic expressions.
ISSN:2331-8422