@article{morton_silverberg_2009, title={Fourier series of half-range functions by smooth extension}, volume={33}, ISSN={["1872-8480"]}, DOI={10.1016/j.apm.2007.12.009}, abstractNote={This paper considers Fourier series approximations of one- and two-dimensional functions over the half-range, that is, over the sub-interval [0, L ] of the interval [− L, L ] in one-dimensional problems and over the sub-domain [0, L x ] × [0, L y ] of the domain [− L x , L x ] × [− L y , L y ] in two-dimensional problems. It is shown how to represent these functions using a Fourier series that employs a smooth extension. The purpose of the smooth extension is to improve the convergence characteristics otherwise obtained using the even and odd extensions. Significantly improved convergence characteristics are illustrated in one-dimensional and two-dimensional problems.}, number={2}, journal={APPLIED MATHEMATICAL MODELLING}, author={Morton, Jeremy and Silverberg, Larry}, year={2009}, month={Feb}, pages={812–821} }