Fourier Series and Orthogonal Polynomials |
Contents
Definition of Fourier series | 1 |
Orthogonality of sines and cosines | 2 |
Determination of the coefficients | 3 |
Copyright | |
52 other sections not shown
Other editions - View all
Common terms and phrases
An+1 applied approaches zero becomes infinite boundary value problem broken-line function Chapter VII coefficients continuous function convergence coordinates corresponding cos² cos²n cosine sum defined definition denoted derivative differential equation equal expression factor finite jumps finite number Fourier series func function f(x function of period graph harmonic harmonic polynomial Hermite polynomials hypothesis identity independent inequality integrand interval Jacobi polynomials Jn(x Jo(x kx dx Laplace series Laplace's equation Lebesgue left-hand member Legendre polynomials Let f(x limit nomials non-negative normalized notation nth degree nth order number of finite obtained orthogonal polynomials orthonormal paragraph partial sum particular Pn(x poly power series proof relation representation respect right-hand member roots satisfies series for f(x sin² Sn(x solution substitution t)dt tion Tn(x trigonometric sum uniformly convergent vanishes weight function x)dx ән ди