Question

The Fourier series of the function $f(x) = \begin{cases} 4x & \text{if } -\pi < x < 0 \\ -2x & \text{if } 0 < x < \pi \end{cases}$ is given by $f(x) \sim c_0 - \sum_{n=0}^{\infty} c_n \cos((2n+1)x) - \sum_{n=1}^{\infty} b_n \sin(nx)$ where $c_0 = -\frac{3\pi}{2}$ $c_n = \frac{6}{\pi(2n+1)^2}$ and $b_n = \frac{2\cos(n\pi)}{n^2\pi}$

Name: the fourier series of the function fx begincases 4x textif pi x 0 2x textif 0 x pi endcases is given by fx sim c0 sumn0infty cn cos2n1x sumn1infty bn sinnx where c0 frac3pi2 cn frac6p 14175
Uploaded: 2024-12-07T18:31:46-08:00
Duration: 4 min 10 s
Channel: Andreas Papavassiliou
Description: the fourier series of the function fx begincases 4x textif pi x 0 2x textif 0 x pi endcases is given by fx sim c0 sumn0infty cn cos2n1x sumn1infty bn sinnx where c0 frac3pi2 cn frac6p 14175

          The Fourier series of the function
$f(x) = \begin{cases} 4x & \text{if } -\pi < x < 0 \\ -2x & \text{if } 0 < x < \pi \end{cases}$
is given by
$f(x) \sim c_0 - \sum_{n=0}^{\infty} c_n \cos((2n+1)x) - \sum_{n=1}^{\infty} b_n \sin(nx)$
where
$c_0 = -\frac{3\pi}{2}$
$c_n = \frac{6}{\pi(2n+1)^2}$
and
$b_n = \frac{2\cos(n\pi)}{n^2\pi}$

$the fourier series of the function fx begincases 4x textif pi x 0 2x textif 0 x pi endcases is given by fx sim c0 sumn0infty cn cos2n1x sumn1infty bn sinnx where c0 frac3pi2 cn frac6p 14175$

Added by Julie P.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Andreas Papavassiliou

12/07/2024

Step 1

Step 1: The given function is $f(x) = \begin{cases} 4x & \text{if } -\pi < x < 0 \\ -2x & \text{if } 0 < x < \pi \end{cases}$ The Fourier series is given by $f(x) \sim c_0 - \sum_{n=0}^{\infty} c_n \cos((2n+1)x) - \sum_{n=1}^{\infty} b_n \sin(nx)$ where $c_0 = Show more…

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The Fourier series of the function $f(x) = \begin{cases} 4x & \text{if } -\pi < x < 0 \\ -2x & \text{if } 0 < x < \pi \end{cases}$ is given by $f(x) \sim c_0 - \sum_{n=0}^{\infty} c_n \cos((2n+1)x) - \sum_{n=1}^{\infty} b_n \sin(nx)$ where $c_0 = -\frac{3\pi}{2}$ $c_n = \frac{6}{\pi(2n+1)^2}$ and $b_n = \frac{2\cos(n\pi)}{n^2\pi}$