How must the form of the approximating polynomials and the formulas for the Fourier coefficients be changed in going from a 2 pi-periodic function to a 2L-periodic function?
For which functions of
period 2L are the Fourier approximations composed entirely of
sine terms? entirely of cosine terms?
How is it possible to approximate a function on [0, L] by a trigonometric polynomial containing only sine terms? only cosine terms?
When does the half-range sine approximation to a continuous function f on [0, L] converge to f at 0?
When does the half-range sine approximation to a continuous function f on [0, L] converge to f at L?
