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cosine_function [2014/01/29 19:51] nikolaj |
cosine_function [2014/03/21 11:11] (current) |
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| ===== Cosine function ===== | ===== Cosine function ===== | ||
| ==== Function ==== | ==== Function ==== | ||
| - | | @#FFBB00: $\mathrm{\cos}: \mathbb C\to\mathbb C$ | | + | | @#FFBB00: definiendum | @#FFBB00: $\mathrm{\cos}: \mathbb C\to\mathbb C$ | |
| - | | @#FFBB00: $\cos(z) := \sum_{k=0}^\infty \frac{(-1)^{k}}{(2k)!}z^{2n} $ | | + | | @#FFBB00: definiendum | @#FFBB00: $\cos(z) := \sum_{k=0}^\infty \frac{(-1)^{k}}{(2k)!}z^{2n} $ | |
| ==== Discussion ==== | ==== Discussion ==== | ||
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| i.e. if $\zeta:=\mathrm e^{i\theta}$, then $\zeta+\overline{\zeta}=2\cos(\theta)$. | i.e. if $\zeta:=\mathrm e^{i\theta}$, then $\zeta+\overline{\zeta}=2\cos(\theta)$. | ||
| ==== Parents ==== | ==== Parents ==== | ||
| - | === Requirements === | + | === Context === |
| [[Infinite sum of complex numbers]], | [[Infinite sum of complex numbers]], | ||
| [[Factorial function]] | [[Factorial function]] | ||
| === Related === | === Related === | ||
| [[Exponential function]], [[Sine function]] | [[Exponential function]], [[Sine function]] | ||
