Helpful formulas for integrating polynomials in three dimensions

He found that the associated optimum formulas had error bounds which were larger by a factor of If or 2 than the optimum for the two parameter family we have been considering. Our computed results indicate further that the minima in these cases are again consistent, and relatively insensitive to changes in the parameter. In practice the different differential equations had errors which corresponded to these results about as they did in the two parameter case. Analogous results were obtained by Johnston [2] for the second and third order methods. A few special cases had been considered earlier by Kuntzmann [3].