Question

Find the fourier series of the function f defined by

f(x) = \begin{Bmatrix} -x^2, -\pi <x\leq 0\\ x^2, 0<x < \pi \end{Bmatrix}

26 Feb 2024
Answer :
Word Count : 261

To find the Fourier series of the function \( f(x) \), we'll need to calculate the coefficients \( a_n \) and \( b_n \) for the Fourier series representation:

\[ f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} \left( a_n \cos(nx) + b_n \sin(nx) \right) \]

The coefficients \( a_n \) and \( b_n \) can be calculated using the formulas:

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