International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2010 
International Tables for Crystallography (2010). Vol. B, ch. 1.3, p. 26

When dealing with functions in n variables and their derivatives, considerable abbreviation of notation can be obtained through the use of multiindices.
A multiindex is an ntuple 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 secondorder partial derivatives: