ThmDex – An index of mathematical definitions, results, and conjectures.
 ▼ Set of symbols ▼ Alphabet ▼ Deduction system ▼ Theory ▼ Zermelo-Fraenkel set theory ▼ Set ▼ Binary cartesian set product ▼ Binary relation ▼ Map ▼ Operation ▼ N-operation ▼ Binary operation ▼ Enclosed binary operation ▼ Groupoid ▼ Semigroup ▼ Standard N-operation ▼ Indexed sum ▼ Series ▼ Power series ▼ Convergent power series ▼ Natural complex exponential function ▼ Complex cosine function
Definition D165
Standard complex cosine function

Let $\mathbb{C}$ be the D372: Set of complex numbers.
The standard complex cosine function is the D4881: Complex function $$\cos : \mathbb{C} \to \mathbb{C}, \quad \cos(z) = \lim_{N \to \infty} \sum_{n = 0}^N (-1)^n \frac{z^{2n}}{(2n)!}$$

Let $\mathbb{C}$ be the D372: Set of complex numbers.
The standard complex cosine function is the D4881: Complex function $$\cos : \mathbb{C} \to \mathbb{C}, \quad \cos(z) = \sum_{n = 0}^{\infty} (-1)^n \frac{z^{2n}}{(2n)!}$$

Let $\mathbb{C}$ be the D372: Set of complex numbers.
The standard complex cosine function is the D4881: Complex function $$\cos : \mathbb{C} \to \mathbb{C}, \quad \cos(z) = \frac{z^0}{0 !} - \frac{z^2}{2 !} + \frac{z^4}{4 !} - \frac{z^6}{6 !} + \cdots$$