let-f-x-be-a-function-period-2pi-such-that-f-x-x-0-lt-x-lt-pi-pi-pi-lt-x-lt-2pi-show-that-the-fourier-series-for-f-x-in-the-interval-0-lt-x-lt-2pi-is-3pi-4-2-pi-cosx-

Question Number 145981 by Gbenga last updated on 10/Jul/21

l e t f (x) b e a f u n c t i o n p e r i o d 2 π s u c h t h a t : f (x) = {x, 0 < x < π

{π, π < x < 2 π

s h o w t h a t t h e f o u r i e r s e r i e s f o r f (x) i n t h e i n t e r v a l 0 < x < 2 π i s

\frac{3 π}{4} - \frac{2}{π} [c o s x + \frac{1}{3^{2}} c o s 3 x + \frac{1}{5^{2}} c o s 5 x + \dots] - [s i n x + \frac{1}{2} s i n 2 x + \frac{1}{3} s i n 3 x + \dots]