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Full-Text Articles in Physical Sciences and Mathematics
Approximation By The K^Lambda Means Of Fourier Series And Conjugate Series Of Functions In H_{Alpha,P}, Ben Landon, Holly Carley, R. N. Mohapatra
Approximation By The K^Lambda Means Of Fourier Series And Conjugate Series Of Functions In H_{Alpha,P}, Ben Landon, Holly Carley, R. N. Mohapatra
Publications and Research
No abstract provided.
Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum, Nataniel Greene
Multiresolution Inverse Wavelet Reconstruction From A Fourier Partial Sum, Nataniel Greene
Publications and Research
The Gibbs phenomenon refers to the lack of uniform convergence which occurs in many orthogonal basis approximations to piecewise smooth functions. This lack of uniform convergence manifests itself in spurious oscillations near the points of discontinuity and a low order of convergence away from the discontinuities.In previous work [11,12] we described a numerical procedure for overcoming the Gibbs phenomenon called the Inverse Wavelet Reconstruction method (IWR). The method takes the Fourier coefficients of an oscillatory partial sum and uses them to construct the wavelet coefficients of a non-oscillatory wavelet series. However, we only described the method standard wavelet series and …
Fourier Series Of Orthogonal Polynomials, Nataniel Greene
Fourier Series Of Orthogonal Polynomials, Nataniel Greene
Publications and Research
Explicit formulas for the Fourier coefficients 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.
Formulas For The Fourier Series Of Orthogonal Polynomials In Terms Of Special Functions, Nataniel Greene
Formulas For The Fourier Series Of Orthogonal Polynomials In Terms Of Special Functions, Nataniel Greene
Publications and Research
An explicit formula for the Fourier coefficient 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 a class of polynomials, including non-orthogonal polynomials.