- For , we get normal Gauss formulae with:
is Legendre Polynomial of degree

**n+1**. - Clearly, Gaussian integration is best when is very hard
to evaluate, and one must minimize value of
**n**. - However, it is very
hard to estimate error in calculation as the simple iterative scheme
described in Section NI.2 for Simpson's rule cannot work.
- Not only is
hard to evaluate weights and 's as
**n**iterates , but you have to recalculate all**n**functions each time. Note: There is no overlap in the values as we double grid points .

Geoffrey Fox, Northeast Parallel Architectures Center at Syracuse University, gcf@npac.syr.edu