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Definition D1931
Standard real sine function

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

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

The standard basic real sine function is the D4364: Real function $$\mathbb{R} \to [-1, 1], \quad x \mapsto x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \frac{x^9}{9!} - \dots$$
Children
 ▶ Standard real cosecant function ▶ Standard real tangent function ▶ Warsaw sine function
Conventions
 ▶ Convention 0 (Notation for standard basic real sine function) The notation used for the D1931: Standard real sine function is $x \mapsto \sin(x)$.