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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
1

Gibbs Phenomenon for Fourier-Legendre Series / Gibbs fenomen för Fourier-Legendre serier

Andersson Svendsen, Joakim January 2023 (has links)
In this thesis, the main objective is to study the presence of Gibbs phenomenon and the Gibbs constant in Fourier-Legendre series. The occurrence of The Gibbs phenomenon is a well known consequence when approximating functions with Fourier series that have points of discontinuity. Consequently, the initial focus was to examine Fourier seriesand the occurrence of Gibbs phenomenon in this context. Next, we delve into Legendrepolynomials, showing their applicability to be expressed as a Fourier series due to theirorthogonality in [−1, 1]. We then continue to explore Gibbs phenomenon for Fourier-Legendre series. The findings proceeds to confirm the existence of the Gibbs phenomenon for Fourier-Legendre series, but most notebly, the values of the error seem to convergeto the same number as for Fourier series which is the Gibbs constant.

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