This paper gives a proof that the polynomial function Qn (s) = ∫so t(t-1) (t-2) • • • (t-n)dt does not change sign on the interval (O,n). Heretofore it was generally believed that Qn (s) changed sign on the interval (O,n) when n was an odd integer. The technique of proof is to show that when n is odd, Qn (s) has an upper bound Qn (n-1) for (n-1)/2 ≤ s ≤ n which is shown to be negative. This result simplifies the treatment of the error terms in certain numerical integration formulas which involve divided differences. The simplified treatment is given here.
Proceedings of the Iowa Academy of Science
©1960 Iowa Academy of Science, Inc.
Lambert, Robert J.
"Error Terms of Numerical Integration Formulas,"
Proceedings of the Iowa Academy of Science, 67(1), 369-381.
Available at: https://scholarworks.uni.edu/pias/vol67/iss1/48