MMfE - Properties of Holomorphic Functions

Properties of Holomorphic Functions

Mathematical_Methods_for_Engineering Theorem

1. $\frac{h(z)}{g(z)}$ is holomorphic for g(z) \neq 0$$\iff $h(z)$ and $g(z)$ are holomorphic.
2. $f(z)=f(x)+if(y)$ is entire (holomorphic in all $\mathbb{C}$) if $f_x+i{f}_y=0$ Where: $f_x=\frac{\partial f(z)}{\partial x}$ $f_y=\frac{\partial f(z)}{\partial y}$
3. ${\int }_{\gamma }f(z)dz={\sum }_i\mathrm{Res}\{f(z),p_o)$ Residue Theorem
   

• What are Holomorphic Functions?

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