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      The Fourier Transforms of the Chebyshev and Legendre Polynomials

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          Abstract

          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.

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          Most cited references10

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          A unified transform method for solving linear and certain nonlinear PDEs

          A. Fokas (1997)
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            On the integrability of linear and nonlinear partial differential equations

            A. Fokas (2000)
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              Two-dimensional linear partial differential equations in a convex polygon

              A. Fokas (2001)
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                Author and article information

                Journal
                21 November 2012
                Article
                1211.4943
                a49deb74-007a-4475-a61a-df8e51235507

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                33C45, 65N35
                17 pages, 2 figures
                math.NA math.AP

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