Multi-index

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Revision as of 16:17, 1 December 2007 by imported>Aleksander Stos (basic definitions)
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In mathematics, multi-index is an n-tuple of non-negative integers. Multi-indices are widely used in multidimensional analysis to denote e.g. partial derivatives and multivariable 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 is defined as

, where

Basic definitions and notational conventions using multi-indices.

  • the order or length of
  • factorial