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\begin{document}
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\begin{equation}
S(z) = -\cos\left(\frac{\pi}{2} z^2\right) \sum_{n=0}^\infty 
     \frac{(-1)^n\pi^{2n+1}}{1\cdot3\cdots(4n+3)} z^{4n+3}
       +\sin\left(\frac{\pi}{2} z^2\right) \sum_{n=0}^\infty
     \frac{(-1)^n\pi^{2n}}{1\cdot3\cdots(4n+1)} z^{4n+1}
\end{equation}
\end{document}