3) Even and Odd Functions in Fourier Series

• Even functions are symmetric about the y-axis, while odd functions are symmetric about the origin.
• Even functions can be represented by a Fourier series with only cosine terms.
• Odd functions can be represented by a Fourier series with only sine terms.
• Any periodic function can be decomposed into an even and odd part, and each part can be represented by a Fourier series.

Important Formulas to Remember in these topic

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- Explanation of Fourier series for even and odd functions in the interval (–π, π):

$$f(x) = \frac{a_0}{2} + \sum_{n=1}^{\infty} a_n\cos(nx) \qquad \text{(even function)}$$

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$$f(x) = \sum_{n=1}^{\infty} b_n\sin(nx) \qquad \text{(odd function)}$$

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