Definition:Half-Range Fourier Sine Series

From ProofWiki
Jump to navigation Jump to search


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

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

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

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

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

Also see