Quadrature formulas for Fourier coefficients

✍ Scribed by Borislav Bojanov; Guergana Petrova

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 774 KB
• Volume: 231
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/j.cam.2009.02.097

✦ Synopsis

We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives.