International
Tables for
Crystallography
Volume B
Reciprocal space
Edited by U. Shmueli

International Tables for Crystallography (2010). Vol. B, ch. 1.3, p. 26   | 1 | 2 |

## Section 1.3.2.2.3. Multi-index notation

G. Bricognea

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#### 1.3.2.2.3. Multi-index notation

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When dealing with functions in n variables and their derivatives, considerable abbreviation of notation can be obtained through the use of multi-indices.

A multi-index is an n-tuple of natural integers: . The length of p is defined asand the following abbreviations will be used:

Leibniz's formula for the repeated differentiation of products then assumes the concise formwhile the Taylor expansion of f to order m about reads

In certain sections the notation will be used for the gradient vector of f, and the notation for the Hessian matrix of its mixed second-order partial derivatives: