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Subtracting out the terms from this expansion allows us to increase the order of convergence, though the terms of this expansion depend on derivatives. Alternatively, we can employ extrapolation methods which achieve higher convergence rates using only the coefficients of the series. We also present a method for the efficient computation of the coefficients in the series.<\/p>","DOI":"10.1090\/s0025-5718-09-02204-2","type":"journal-article","created":{"date-parts":[[2009,4,27]],"date-time":"2009-04-27T13:47:33Z","timestamp":1240840053000},"page":"1629-1645","source":"Crossref","is-referenced-by-count":18,"title":["On the convergence rate of a modified Fourier series"],"prefix":"10.1090","volume":"78","author":[{"given":"Sheehan","family":"Olver","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2009,2,18]]},"reference":[{"key":"1","series-title":"National Bureau of Standards Applied Mathematics Series, No. 55","volume-title":"Handbook of mathematical functions with formulas, graphs, and mathematical tables","author":"Abramowitz, Milton","year":"1964"},{"key":"2","doi-asserted-by":"crossref","unstructured":"Aksenov, S., Savageau, M.A., Jentschura, U.D., Becher, J., Soff, G., Mohr, P.J., Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics, Comp. 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