CHAPTER 16 - Different Forms of Fourier Series

Abstract

This chapter describes the different forms of Fourier series. The Fourier series for f(x) on -L ≤ x ≤ L is defined in the chapter. If f(x) is periodic with period 2L the Fourier series represents f(x) for all x and these integrals may be evaluated over any interval of length 2L. The half-range Fourier cosine series for f(x) on 0 ≤ x ≤ π is described in the chapter. If f (x) is an even function, or it is extended to the interval π ≤ x ≤ π as an even function so that f(x ) = f(-x), the Fourier series represents f(x) on the interval -π ≤ x ≤ π. The complex (exponential) Fourier series for f(x) on -π ≤ x ≤ π is also elaborated in the chapter.