Prove-that-for-pi-2-lt-x-lt-pi-2-1-1-3-cos-x-1-3-3-cos-3x-1-5-3-cos-5x-to-infinity-pi-8-pi-2-4-x-2-

Question Number 13806 by ajfour last updated on 23/May/17

P r o v e t h a t f o r - \frac{π}{2} < x < \frac{π}{2},

\frac{1}{1^{3}} \cos x - \frac{1}{3^{3}} \cos 3 x + \frac{1}{5^{3}} \cos 5 x - \dots . t o i n f i n i t y

= \frac{π}{8} (\frac{π^{2}}{4} - x^{2}) .

Commented by prakash jain last updated on 24/May/17

LHS looks like fourier series

expansion .

I will look for appropriate function

to start with .