Trigonometric series

A trigonometric series is a series of the form:

A_{0}+\displaystyle\sum_{n=1}^{\infty}(A_{n} \cos{nx} + B_{n} \sin{nx}).

It is called a Fourier series if the terms $A_{n}$ and $B_{n}$ have the form:

A_{n}=\frac{1}{\pi}\displaystyle\int^{2 \pi}_0\! f(x) \cos{nx} \,dx\qquad (n=0,1,2,3 \dots)

B_{n}=\frac{1}{\pi}\displaystyle\int^{2 \pi}_0\! f(x) \sin{nx}\, dx\qquad (n=1,2,3, \dots)

where $f$ is an integrable function.

单词	Trigonometrical Series
释义	Trigonometrical Series 英语百科 Trigonometric series A trigonometric series is a series of the form: $A_{0}+\displaystyle\sum_{n=1}^{\infty}(A_{n} \cos{nx} + B_{n} \sin{nx}).$ It is called a Fourier series if the terms $A_{n}$ and $B_{n}$ have the form: $A_{n}=\frac{1}{\pi}\displaystyle\int^{2 \pi}_0\! f(x) \cos{nx} \,dx\qquad (n=0,1,2,3 \dots)$ $B_{n}=\frac{1}{\pi}\displaystyle\int^{2 \pi}_0\! f(x) \sin{nx}\, dx\qquad (n=1,2,3, \dots)$ where $f$ is an integrable function.
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Trigonometrical Series