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| Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
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exponential_function [2015/12/09 16:06] nikolaj |
exponential_function [2016/07/10 15:04] nikolaj |
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| ^ $\mathrm{e}^z \neq 0 $ ^ | ^ $\mathrm{e}^z \neq 0 $ ^ | ||
| - | ^ $\frac{\mathrm d}{\mathrm d z}\mathrm{e}^{f(z)} = \frac{\mathrm d}{\mathrm d z}f(z)\cdot \mathrm{e}^{f(z)} $ ^ | + | ^ $\frac{\mathrm d}{\mathrm d z}\mathrm{e}^{f(z)} = \frac{\mathrm d}{\mathrm dz}f(z)\cdot \mathrm{e}^{f(z)} $ ^ |
| $a,b,r,\theta\in\mathbb R$ | $a,b,r,\theta\in\mathbb R$ | ||
| Line 26: | Line 26: | ||
| $\left(x+y\right)^m=\sum_{k=0}^m \dfrac{n!}{k!\,(m-k)!} x^k y^{m-k}$ | $\left(x+y\right)^m=\sum_{k=0}^m \dfrac{n!}{k!\,(m-k)!} x^k y^{m-k}$ | ||
| + | |||
| + | so | ||
| + | |||
| + | $\left(1 + b_n\,x \right)^n = \sum_{k=0}^n \left( \dfrac {1} {b_n^k}\dfrac {n!} {(n-k)!} \right) \dfrac {x^k} {k!}$ | ||
| so | so | ||
