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}).](/Images/godic/202502/17/3e27bf4378a570614c89dc6ba65b50320900.png")
It is called a Fourier series if the terms ![A_{n}](/Images/godic/202502/17/2e03ac601b07640385118777cae003440900.png")
and ![B_{n}](/Images/godic/202502/17/0d920f2fec375babdcf7c4e2a8b84d200900.png")
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)](/Images/godic/202502/17/336622a6b6d707d8472a183616951f720900.png")
![B_{n}=\frac{1}{\pi}\displaystyle\int^{2 \pi}_0\! f(x) \sin{nx}\, dx\qquad (n=1,2,3, \dots)](/Images/godic/202502/17/479853d43630ca36fc071281a3b114980900.png")
where ![f](/Images/godic/202502/17/8fa14cdd754f91cc6554c9e71929cce70900.png")
is an integrable function.
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