is also that of all functions of the form (1 + x2)-2N-c+lQ(x) where Q is a polynomial of degree 4N 2 or lower, the conditions determining the above formula for any a and N are the same as those determining Harper's formula for (using "k" and "n" in the meaning given them in [1]) k = a + 2N -2, n = 2N. Thus we have just re-derived Harper's formulas for even n. It follows from known properties of Jacobi-Gauss quadrature that the coefficients are non-negative; and if f is continuous and a is chosen large enough to make g bounded, it follows that the approximation obtained converges to the integral as N increases.