\[(-1)^{\left\lfloor n/2\right\rfloor-1}\frac{(2\pi)^{n}}{2(n!)}B_{n}\left(x%
\right)\to\begin{cases}\cos\left(2\pi x\right),&n\text{ even},\\
\sin\left(2\pi x\right),&n\text{ odd},\end{cases}\]