 The weights can be expressed as

where formula_23 is the coefficient of formula_24 in formula_25.To prove this, note that using Lagrange interpolation one can express in terms of formula_26 as

because has degree less than and is thus fixed by the values it attains at different points.Multiplying both sides by and integrating from to yields

The weights are thus given by

This integral expression for formula_30 can be expressed in terms of the orthogonal polynomials formula_31 and formula_32 as follows.