Can a fourier series of a function just be a constant?

Thread starter schattenjaeger
Start date Oct 23, 2005
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Constant Fourier Fourier series Function Series

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A Fourier series can indeed reduce to a constant when the original function is constant, resulting in a non-zero a0 and zero coefficients for an and bn. This situation occurs because the constant function does not vary with x, leading to no sine or cosine components. The constant value represents the average of the function over the interval. Therefore, the Fourier series simplifies to just the constant term a0. This highlights the relationship between the nature of the original function and its Fourier series representation.

Oct 23, 2005

schattenjaeger

say if you get a result for a0 but 0 for an and bn(using my book's notation where the Fourier series is a0+an*cos(nx)+bn*sin(nx)

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Oct 24, 2005

Galileo

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Ofcourse. It happens when the original function is constant.

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