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Definition D1927
Standard real cosine function

The standard real cosine function is the D4364: Real function $$\mathbb{R} \to [-1, 1], \quad x \mapsto \lim_{N \to \infty} \sum_{n = 0}^N (-1)^n \frac{x^{2n}}{(2n)!}$$

The standard real cosine function is the D4364: Real function $$\mathbb{R} \to [-1, 1], \quad x \mapsto \sum_{n = 0}^{\infty} (-1)^n \frac{x^{2n}}{(2n)!}$$

The standard real cosine function is the D4364: Real function $$\mathbb{R} \to [-1, 1], \quad x \mapsto 1 - \frac{x^2}{2!} + \frac{x^4}{4!} - \frac{x^6}{6!} + \frac{x^8}{8!} - \dots$$
Children
 ▶ D1583: Weierstrass function
Conventions
 ▶ Convention 0 (Notation for standard basic real cosine function) The notation used for the D1927: Standard real cosine function is $x \mapsto \cos(x)$.