Definition:Half-Range Fourier Sine Series/Range Pi

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Definition

Let $\map f x$ be a real function defined on the interval $\openint 0 \pi$.


Then the half-range Fourier sine series of $\map f x$ over $\openint 0 \pi$ is the series:

$\map f x \sim \displaystyle \sum_{n \mathop = 1}^\infty b_n \sin n x$

where for all $n \in \Z_{> 0}$:

$b_n = \displaystyle \frac 2 \pi \int_0^\pi \map f x \sin n x \rd x$


Also see


Sources