Zeitblom said:I have to find the Fourier series of f(x)=sin(2x)
but i always get all the coefficients (a0, an and bn) equal zero.
is it right?
Thank you
A Fourier series is a mathematical representation of a periodic function as an infinite sum of sinusoidal functions. It is used to decompose a complex function into simpler components.
The Fourier series of Sin(2x) can be found by applying the Fourier series formula, which involves calculating the coefficients of the sine function using integration. In this case, the coefficients will be 0 for all even terms and 2/pi for all odd terms.
The period of the Fourier series of Sin(2x) is π, which is the same as the period of the original function Sin(2x).
The Fourier series of Sin(2x) converges to the function Sin(2x) for all values of x. However, it converges faster for some values of x than others, leading to the phenomenon of Gibbs oscillations near the discontinuity points of the function.
The Fourier series of Sin(2x) has various applications in fields such as signal processing, image processing, and physics. It is used to analyze and manipulate complex periodic signals and to solve differential equations in physics.