Definition:Sine/Complex Function

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Definition

The complex function $\sin: \C \to \C$ is defined as:

\(\displaystyle \sin z\) \(=\) \(\displaystyle \sum_{n \mathop = 0}^\infty \paren {-1}^n \frac {z^{2 n + 1 } } {\paren {2 n + 1}!}\)
\(\displaystyle \) \(=\) \(\displaystyle z - \frac {z^3} {3!} + \frac {z^5} {5!} - \frac {z^7} {7!} + \cdots + \paren {-1}^n \frac {z^{2 n + 1 } } {\paren {2 n + 1}!} + \cdots\)


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