Multi-index

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Revision as of 13:52, 4 December 2007 by imported>Aleksander Stos (more notation...)
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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 of a multi-index
  • multidimensional power notation
If and is a multi-index then is defined as
  • The following notation are used to denote a partial derivative of a function
Remark: sometimes instead of is used as well.