A new Taylor like expansion formula is established. Here the Riemann-Stieltjes integral of a function is expanded into a finite sum form which involves the derivatives of the function evaluated at the right end point of the interval of integration. The error of the approximation is given in an integral form involving the 𝑛th derivative of the function. Implications and applications of the formula follow.
@article{1706,
title = {A New Expansion Formula},
journal = {CUBO, A Mathematical Journal},
volume = {5},
year = {2003},
language = {en},
url = {http://dml.mathdoc.fr/item/1706}
}
Anastassiou, George A. A New Expansion Formula. CUBO, A Mathematical Journal, Tome 5 (2003) . http://gdmltest.u-ga.fr/item/1706/