 The error of a Gaussian quadrature rule can be stated as follows .For an integrand which has continuous derivatives,

for some in , where is the monic (i.e.the leading coefficient is ) orthogonal polynomial of degree and where

In the important special case of , we have the error estimate 

Stoer and Bulirsch remark that this error estimate is inconvenient in practice, since it may be difficult to estimate the order derivative, and furthermore the actual error may be much less than a bound established by the derivative.