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

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

The standard real cosine function is the D4364: Real function \begin{equation} \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 \end{equation}