Differences
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holomorphic_function [2015/01/29 13:05] nikolaj |
holomorphic_function [2015/01/29 13:05] nikolaj |
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| For functions like the complex conjugation, $f(z):=\overline{z}$, the finite difference | For functions like the complex conjugation, $f(z):=\overline{z}$, the finite difference | ||
| - | $\dfrac{f(z)-f(0)}{z-0}=\dfrac{\overline{z}}{z}={\mathrm e}^{-2i\mathrm{arg}(z)}$ | + | $\dfrac{f(z)-f(0)}{z-0}=\dfrac{\overline{z}}{z}={\mathrm e}^{-2i\,\mathrm{arg}(z)}$ |
| varies strongly with the $z$'s argument, even if $z$ is varied in only an arbitrarily small area around $0$, and so there is no limit. The function $f$ doesn't have a derivative. | varies strongly with the $z$'s argument, even if $z$ is varied in only an arbitrarily small area around $0$, and so there is no limit. The function $f$ doesn't have a derivative. | ||
