Difference between revisions of "Taylor series of sine"
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| − | <strong>[[Taylor series of sine| | + | <strong>[[Taylor series of sine|Theorem]]:</strong> Let $z_0 \in \mathbb{C}$. The following [[Taylor series]] holds: |
| − | $$\sin(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^ | + | $$\sin(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k(z-z_0)^{2k+1}}{(2k+1)!},$$ |
where $\sin$ denotes the [[sine]] function. | where $\sin$ denotes the [[sine]] function. | ||
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Revision as of 06:22, 25 March 2016
Theorem: Let $z_0 \in \mathbb{C}$. The following Taylor series holds: $$\sin(z)=\displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k(z-z_0)^{2k+1}}{(2k+1)!},$$ where $\sin$ denotes the sine function.
Proof: █
