We prove that the only functions for which certain standard numerical integration formulas are exact are polynomials.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am31-1-1,
author = {Pawe\l\ Szeptycki},
title = {Integration of polynomials},
journal = {Applicationes Mathematicae},
volume = {31},
year = {2004},
pages = {1-4},
zbl = {1072.41017},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am31-1-1}
}
Paweł Szeptycki. Integration of polynomials. Applicationes Mathematicae, Tome 31 (2004) pp. 1-4. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am31-1-1/