This is an old revision of the document!
Multi-index power
Definition
| $ G $ … group |
| $ g \in \text{Sequence}(G) $ |
| $ \alpha \in \text{Sequence}(\mathbb N) $ |
| $ \mathrm{length}(g)=\mathrm{length}(\alpha) $ |
| $ \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: Multi-index notation
Parents
Requirements
