Multi-index
From Knowino
In mathematics, multi-index is an n-tuple of non-negative integers. Multi-indices are widely used in multivariable analysis to denote e.g. partial derivatives and multidimensional power function. Many formulas known from the one dimension one (i.e. the real line) carry on to by simple replacing usual indices with multi-indices.
Formally, multi-index α is defined as
- , where
Basic definitions and notational conventions using multi-indices.
- The order or length of α
- Factorial of a multi-index
- multidimensional power notation
- If and is a multi-index then xα is defined as
- The following notation is used for partial derivatives of a function
- Remark: sometimes the symbol instead of Dα is used.
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