Error Terms of Numerical Integration Formulas

Authors

Robert J. Lambert, Iowa State University

Document Type

Research

Abstract

This paper gives a proof that the polynomial function Q_n (s) = ∫^s_o t(t-1) (t-2) • • • (t-n)dt does not change sign on the interval (O,n). Heretofore it was generally believed that Q_n (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, Q_n (s) has an upper bound Q_n (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.

Publication Date

1960

Journal Title

Proceedings of the Iowa Academy of Science

Volume

67

Issue

1

First Page

369

Last Page

381

Copyright

©1960 Iowa Academy of Science, Inc.

Language

en

File Format

application/pdf

Recommended Citation

Lambert, Robert J. (1960) "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