multi-index notation

With the multi-index notation the rule states more generally:

Here, sup denotes the supremum, and we again use multi-index notation.

We will use the multi-index notation:

The multi-index notation allows the extension of many formulae from elementary calculus to the corresponding multi-variable case.

To start with the geometry, the Bombieri scalar product for homogeneous polynomials with N variables can be defined as follows using multi-index notation: