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What is the Fourier sine series for sin(pix/a) where 0 < x < a?

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Final answer:

The Fourier sine series for sin(pix/a) can be expressed using a series of cosine functions with different coefficients and frequencies.

Step-by-step explanation:

The Fourier sine series for sin(pix/a) where 0 < x < a can be expressed as:

sin(pix/a) = (4a/π) * (1 - 1/3 * cos(2πx/a) + 1/5 * cos(4πx/a) - 1/7 * cos(6πx/a) + ...)

In this series, the coefficients represent the amplitudes of the harmonics at different frequencies. The terms with even powers of cosine correspond to odd harmonics, while the terms with odd powers of cosine correspond to even harmonics.

User Jim Cownie
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