\begin{definition}[Definition:Half-Range Fourier Cosine Series/Formulation 1]
Let $\map f x$ be a real function defined on the interval $\openint 0 \lambda$.
Then the ''' half-range Fourier cosine series''' of $\map f x$ over $\openint 0 \lambda$ is the series:
:$\map f x \sim \dfrac {a_0} 2 + \ds \sum_{n \mathop = 1}^\infty a_n \cos \frac {n \pi x} \lambda$
where for all $n \in \Z_{\ge 0}$:
:$a_n = \ds \frac 2 \lambda \int_0^\lambda \map f x \cos \frac {n \pi x} \lambda \rd x$
\end{definition}