The Gateway to Computer Science Excellence
First time here? Checkout the FAQ!
x
+1 vote
380 views

Fourier series of the periodic function (period 2π) defined by

$$f(x) = \begin{cases} 0, -p < x < 0\\x, 0 < x < p \end{cases} \text { is }\\ \frac{\pi}{4} + \Sigma \left [ \frac{1}{\pi n^2} \left(\cos n\pi - 1 \right) \cos nx - \frac{1}{n} \cos n\pi \sin nx \right ]$$

But putting $x = \pi$, we get the sum of the series

$$ 1 + \frac{1}{3^2} + \frac{1}{5^2} + \frac{1}{7^2} + \cdots \text { is }$$ 

  1. $\frac{{\pi }^2 }{4}$
  2. $\frac{{\pi }^2 }{6}$
  3. $\frac{{\pi }^2 }{8}$
  4. $\frac{{\pi }^2 }{12}$
asked in Calculus by (65 points) | 380 views

1 Answer

0 votes

First of all, Fourier series of given function is calculated wrong here.

Refer This :


answered by (11 points)

Related questions



Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true

39,828 questions
46,802 answers
140,987 comments
58,944 users