Changes

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

:<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 other classes of functions, for instance the space <math>L^2(\mathbb R^n)</math>[[square integrable function]]s.  Even more generally, it is possible to carry out Fourier analysis in the setting of [[compact space|locally compact]] [[abelian]] [[topology|topological]] [[group|groups]], where the fundamental observation of Pontryagin duality provides the necessary theoretical underpinnings.   

Fourier series can be generalized to [[Fourier transformation]]s for other classes of functions, for instance the space <math>L^2(\mathbb R^n)</math> of [[square integrable function]]s.  Even more generally, it is possible to carry out Fourier analysis in the setting of [[compact space|locally compact]] [[abelian]] [[topology|topological]] [[group|groups]], where the fundamental observation of Pontryagin duality provides the necessary theoretical underpinnings.   

[[category:Calculus]]

[[category:Calculus]]