I'm studying Fourier Series and Discrete Fourier Transform, and I have a conceptual question.
The complex form of the Fourier Series is: $$ f(t) = \sum_{n=-\infty}^{\infty} c_n e^{i\omega_n t} $$ and to find the coefficient the following formula is used: $$ c_n = \frac{1}{2\pi} \int_0^{2\pi} \! f(t) \, e^{-i\omega_n t} \, dt $$
My question is: Is this formula above the Discrete Fourier Transform or not?
If she is not the Discrete Fourier Transform what is she then?