The traditional sawtooth is written as
$\frac{A}{2}-\frac {A}{\pi}\sum_{k=1}^{\infty}\frac {\sin (2\pi kft)}{k}$
The general formula is given as
\begin{equation} s(x) = \frac{a_0}{2} + \sum_{n=1}^\infty \left[a_n\cos\left(nx\right)+b_n\sin\left(nx\right)\right] \\ =\frac{2}{\pi}\sum_{n=1}^\infty \frac{(-1)^{n+1}}{n} \sin(nx), \quad \mathrm{for} \quad x - \pi \notin 2 \pi \mathbf{Z}. \end{equation}
What is the "rule" for the coefficients? This is $a_{0}$ for all odd coefficients and all b coefficients equal to zero?
Is there a resource you could recommend which explains this process?