The Gibbs' phenomenon for Fourier-Bessel series
Fay, Temple H. Kloppers, P. Hendrik
Fay, Temple H.
Kloppers, P. Hendrik
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Abstract
The paper investigates the Gibbs’ phenomenon at a jump discontinuity for Fourier–Bessel series expansions. The unexpected thing is that the Gibbs’ constant for Fourier–Bessel series appears to be the same as that for Fourier series expansions. In order to compute the coefficients for Fourier–Bessel functions efficiently, several integral formulas are derived and the Struve functions and their asymptotic expansions discussed, all of which significantly ease the computations. Three numerical examples are investigated. Findings suggest further investigations suitable for undergraduate research projects or small student group investigations.
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Date
2010-11-11
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Taylor and Francis
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Keywords
Gibbs’ phenomenon, Fourier–Bessel, Numerical, Sturm–Liouville, Equations