Power Series for Complex Variables

Tags: #math #complex variables

Equation

$$\begin{gathered} e^z=1+z+\frac{z^2}{2!}+\frac{z^3}{3!}+...+\frac{z^n}{n!}+... \\ \sin z=z-\frac{z^3}{3!}+\frac{z^5}{5!}-... \\ \cos z=1-\frac{z^2}{2!}+\frac{z^4}{4!}-... \\ \ln (1+z)=1-\frac{z^2}{2!}+\frac{z^3}{3!}-... \\ (1+z{)}^n=1+nz+\frac{n(n-1)}{2!}{z}^2+\frac{n(n-1)(n-2)}{3!}{z}^3+... \end{gathered}$$

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