Gregory,s Formula

Gregory's formula is a formula that allows a definite integral of a function to be expressed by its sum and differences, or its sum by its integral and difference (Jordan 1965, p. 284). It is given by the equation

discovered by Gregory in 1670 and reported to be the earliest formula in numerical integration (Jordan 1965, Roman 1984).

REFERENCES:

Jordan, C. "Gregory's Summation Formula." §99 in Calculus of Finite Differences, 3rd ed. New York: Chelsea, pp. 284-287, 1965.

Roman, S. The Umbral Calculus. New York: Academic Press, p. 59, 1984.