 But all terms involving formula_82 for vanish when integrated from −1 to 1, leaving only the "k"th term.In these few lines, which are close to the modern formalism used in Fourier series, Fourier revolutionized both mathematics and physics.Although similar trigonometric series were previously used by Euler, d'Alembert, Daniel Bernoulli and Gauss, Fourier believed that such trigonometric series could represent any arbitrary function.