On the Euler-Maclaurin formula
Using the distributional theory of asymptotic expansions, new Euler-Maclaurin type formulas for numerical quadratures based on generalized functions are derived. The expansions for functions with fractional power behavior at the endpoints is obtained. The development for functions with discontinuities is also considered and the appearance of oscillatory functions as coefficients is observed.
Publication Source (Journal or Book title)
Boletin de la Sociedad Matematica Mexicana
Estrada, R. (1997). On the Euler-Maclaurin formula. Boletin de la Sociedad Matematica Mexicana, 3 (1), 117-133. Retrieved from https://digitalcommons.lsu.edu/mathematics_pubs/319