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Multi-Index Notation

Multi-index notation is used to shorten expressions that contain many indices. Let x in R^n and write x=(x_1,...,x_n). A multi-index alpha is an n-tuple of integers alpha_j with j=1, ..., n. The notation |alpha| is used to denote the length alpha_1+...+alpha_n.

For monomial expressions in coordinates x_i, multi-index notation provides a convenient shorthand. For example, writing x^alpha=x_1^(alpha_1)...x_n^(alpha_n), gives a compact notation

(partial^(|alpha|))/(partialx^alpha)=(partial^(alpha_1))/(partialx_1^(alpha_1))...(partial^(alpha_n))/(partialx_n^(alpha_n))

for the partial derivative.

See also

Index, Index Set

This entry contributed by W.D. Van Suijlekom

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Cite this as:

Suijlekom, W.D. Van. "Multi-Index Notation." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/Multi-IndexNotation.html

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