Definition:Half-Range Fourier Cosine Series/Formulation 2

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

Then the  half-range Fourier cosine series of $\map f x$ over $\openint a b$ is the series:


 * $\ds \map f x \sim \frac {A_0} 2 + \sum_{m \mathop = 1}^\infty A_m \cos \frac {m \pi \paren {x - a} } {b - a}$

where for all $m \in \Z_{\ge 0}$:
 * $A_m = \ds \frac 2 {b - a} \int_a^b \map f x \cos \frac {m \pi \paren {x - a} } {b - a} \rd x$