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The word weight has many uses in mathematics. It can refer to a function 
(also called a Weighting Function or
Weight Function) used to normalize Orthonormal Functions. It can also be used to indicate one of a set of a
multiplicative constants placed in front of terms in a Moving Average, Newton-Cotes Formulas, edge or vertex of
a Graph or Tree, etc.
See also Weighted Tree, Weighting Function