A Fifth Degree Integration Formula for the n-Simplex

For n = 2 this 7-point formula was given by Hammer, Marlowe and Stroud [1]. For n ? 3 this formula is new. The right side of (1) will be denoted by the symbol En(f). In ? 2 we define the points which we use in (1). These points vi are the common zeros of a certain set of orthogonal polynomials for 7n. With these points we show in ? 3 that we can find coefficients Ai such that En(f) has degree 5. Only 5 of the Ai are distinct and we tabulate these for 3 3). This formula is given in ? 4. It is an approximation,