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multi-index_power [2013/09/17 00:23] nikolaj |
multi-index_power [2013/09/17 00:24] nikolaj |
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| | @#FFBB00: $ \langle g,\alpha\rangle \mapsto g^\alpha := \prod_{i=1}^{\mathrm{length}(\alpha)} g_i^{\alpha_i} $ | | | @#FFBB00: $ \langle g,\alpha\rangle \mapsto g^\alpha := \prod_{i=1}^{\mathrm{length}(\alpha)} g_i^{\alpha_i} $ | | ||
| - | We also write $|\gamma|=\sum_i^{\mathrm{length} \gamma_i $. | + | We also write $|\gamma|=\sum_i^{\mathrm{length}(\gamma)} \gamma_i $. |
| ==== Discussion ==== | ==== Discussion ==== | ||
| Line 15: | Line 15: | ||
| $\gamma=\langle 3,1,0,0,2 \rangle$ | $\gamma=\langle 3,1,0,0,2 \rangle$ | ||
| - | is taken to be a multiindex, then we write | + | is taken to be a multiindex, then $|\gamma|=6$ and we write |
| - | $|\gamma|=6$ and | + | $f^{(\gamma)}(x) \equiv \frac{\partial^{|\gamma|}}{\partial x^\gamma} f \equiv \frac{\partial^3}{\partial x_1^3} \frac{\partial}{\partial x_2} \frac{\partial^2}{\partial x_5^2} f $ |
| - | + | ||
| - | $f^{(\gamma)}(x) \equiv \frac{\partial^{|\gamma|}}{\partial x\gamma} f \equiv \frac{\partial^3}{\partial x_1^3} \frac{\partial}{\partial x_2} \frac{\partial^2}{\partial x_5^2} f $ | + | |
| === Reference === | === Reference === | ||
