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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