Changes

:<math> f(t) = \frac{1}{2} a_0 + \sum_{n=1}^{\infty}[a_n \cos(\omega_n t) + b_n \sin(\omega_n t)] </math>

:<math> f(t) = \frac{1}{2} a_0 + \sum_{n=1}^{\infty}[a_n \cos(\omega_n t) + b_n \sin(\omega_n t)] </math>

where, ''n'' is an integer and

where, ''n'' is an integer and

:<math> \omega_n = n\frac{2\pi}{T}</math> &nbsp; &nbsp;

:<math> \omega_n = n\frac{2\pi}{T}</math>

:<math>a_n = \frac{2}{T} \int_{t_1}^{t_2} f(t) \cos(\omega_n t)\, dt</math> &nbsp; &nbsp;

:<math>a_n = \frac{2}{T} \int_{t_1}^{t_2} f(t) \cos(\omega_n t)\, dt</math>

:<math>b_n = \frac{2}{T} \int_{t_1}^{t_2} f(t) \sin(\omega_n t)\, dt </math> &nbsp; &nbsp;

:<math>b_n = \frac{2}{T} \int_{t_1}^{t_2} f(t) \sin(\omega_n t)\, dt </math>

Fourier series can be generalized to [[Fourier transformation]]s for non-perodic, piecewise continuous, [[square integrable function]]s.

Fourier series can be generalized to [[Fourier transformation]]s for non-perodic, piecewise continuous, [[square integrable function]]s.

[[category: mathematics]]

[[category: mathematics]]