We obtain exponentially accurate Fourier series for nonperiodic functions on the interval [−1, 1] by extending these functions to periodic functions on a larger domain. The series may be evaluated, ...

THE theory of functions of a real variable is a subject of fairly recent date and is necessarily expanding as new theorems are discovered and fresh generalisations effected. On the other hand, the ...

A mathematical theorem stating that a PERIODIC function f(x) which is reasonably continuous may be expressed as the sum of a series of sine or cosine terms (called the Fourier series), each of which ...

This is a preview. Log in through your library . Abstract In the present paper we generalize Eckhoff's method, i.e., the method for approximating the locations of discontinuities and the associated ...