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Document Type

Research

Abstract

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.

Publication Date

1960

Journal Title

Proceedings of the Iowa Academy of Science

Volume

67

Issue

1

First Page

369

Last Page

381

Copyright

© Copyright 1960 by the Iowa Academy of Science, Inc.

Language

EN

File Format

application/pdf

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