let f(x) be a function period 2π such that:f(x)={x, 0<x<π {π, π<x<2π show that the fourier series for f(x) in the interval 0<x<2π is ((3π)/4)−(2/π)[cosx+(1/3^2 )cos3x+(1/5^2 )cos5x+...]−[sinx+(1/2)sin2x+(1/3)sin3x+...]


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Question Number 145981 by Gbenga last updated on 10/Jul/21
$let f(x) be a function period 2π such that:f(x)={x, 0<x<π {π, π<x<2π show that the fourier series for f(x) in the interval 0<x<2π is ((3π)/4)−(2/π)[cosx+(1/3^2 )cos3x+(1/5^2 )cos5x+...]−[sinx+(1/2)sin2x+(1/3)sin3x+...]$
$l e t f (x) b e a f u n c t i o n p e r i o d 2 π s u c h t h a t : f (x) = {x, 0 < x < π$ ${π, π < x < 2 π$ $s h o w t h a t t h e f o u r i e r s e r i e s f o r f (x) i n t h e i n t e r v a l 0 < x < 2 π i s$ $\frac{3 π}{4} - \frac{2}{π} [c o s x + \frac{1}{3^{2}} c o s 3 x + \frac{1}{5^{2}} c o s 5 x + . . .] - [s i n x + \frac{1}{2} s i n 2 x + \frac{1}{3} s i n 3 x + . . .]$
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