\begin{definition}[Definition:Half-Range Fourier Sine Series/Formulation 1]
Let $\map f x$ be a real function defined on the interval $\openint 0 \lambda$.
Then the '''half-range Fourier sine series''' of $\map f x$ over $\openint 0 \lambda$ is the series:
:$\map f x \sim \ds \sum_{n \mathop = 1}^\infty b_n \sin \frac {n \pi x} \lambda$
where for all $n \in \Z_{> 0}$:
:$b_n = \ds \frac 2 \lambda \int_0^\lambda \map f x \sin \frac {n \pi x} \lambda \rd x$
\end{definition}