Multi-index
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Revision as of 12:52, 16 November 2011 by Boris Tsirelson (talk | contributions)
In mathematics, multi-index is an n-tuple of non-negative integers. Multi-indices are widely used in multivariable calculus to denote e.g. partial derivatives and multidimensional power function. Many formulas known from the univariable calculus (i.e. over 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 is the product
- multidimensional power notation
- If and is a multi-index then x^{α} is defined as the product
- The following notation is used for partial derivatives of a function
- Remark: sometimes the symbol instead of D^{α} is used.
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