===== Multi-index power =====
==== Set ====
| @#55CCEE: context     | @#55CCEE: $ G $ ...  group |
| @#55CCEE: context     | @#55CCEE: $ g \in \text{Sequence}(G) $ |
| @#55CCEE: context     | @#55CCEE: $ \alpha \in \text{Sequence}(\mathbb N) $ |
| @#55CCEE: context     | @#55CCEE: $ \mathrm{length}(g)=\mathrm{length}(\alpha) $ |

| @#FFBB00: definiendum | @#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 ====
=== Context ===
[[Group]], [[Integer]], [[Sequence length]]