Multi-index Notation - Multi-index Notation

Multi-index Notation

An n-dimensional multi-index is an n-tuple

of non-negative integers (i.e. an element of the n-dimensional set of natural numbers, denoted ).

For multi-indices and one defines:

Componentwise sum and difference
Partial order
Sum of components (absolute value)
Factorial
Binomial coefficient
Multinomial coefficient

where .

Power
.
Higher-order partial derivative

where (see also 4-gradient).

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