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multi-index_power [2013/09/17 00:24]
nikolaj
multi-index_power [2014/03/21 11:11]
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-===== Multi-index power ===== 
-==== Definition ==== 
-| @#88DDEE: $ G $ ...  group | 
-| @#88DDEE: $ g \in \text{Sequence}(G) $ | 
-| @#88DDEE: $ \alpha \in \text{Sequence}(\mathbb N) $ | 
-| @#88DDEE: $ \mathrm{length}(g)=\mathrm{length}(\alpha) $ | 
  
-| @#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)} \gamma_i $. 
- 
-==== Discussion ==== 
-In most cases, the base sequence is understood. E.g. if  
- 
-$\gamma=\langle 3,1,0,0,2 \rangle$ ​ 
- 
-is taken to be a multiindex, then $|\gamma|=6$ and we write 
- 
-$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 === 
-Wikipedia: [[http://​en.wikipedia.org/​wiki/​Multi-index_notation|Multi-index notation]] 
-==== Parents ==== 
-=== Requirements === 
-[[Group]], [[Integer]],​ [[Sequence length]] 
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