Difference between revisions of "Taylor series of cosine"
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| − | <strong>[[Taylor series of cosine|Theorem]]:</strong> Let $z_0 \in \mathbb{C}$. The following [[Taylor series]] holds: | + | <strong>[[Taylor series of cosine|Theorem]]:</strong> Let $z_0 \in \mathbb{C}$. The following [[Taylor series]] holds for all $z \in \mathbb{C}$: |
$$\cos(z)= \displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k (z-z_0)^{2k}}{(2k)!},$$ | $$\cos(z)= \displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k (z-z_0)^{2k}}{(2k)!},$$ | ||
where $\cos$ denotes the [[cosine]] function. | where $\cos$ denotes the [[cosine]] function. | ||
Revision as of 06:24, 25 March 2016
Theorem: Let $z_0 \in \mathbb{C}$. The following Taylor series holds for all $z \in \mathbb{C}$: $$\cos(z)= \displaystyle\sum_{k=0}^{\infty} \dfrac{(-1)^k (z-z_0)^{2k}}{(2k)!},$$ where $\cos$ denotes the cosine function.
Proof: █
