Gregory's series
Encyclopedia
Gregory's series, also known as the Madhava-Gregory series or Leibniz's series, is a mathematical series
that was discovered by the Indian mathematician Madhava of Sangamagrama
(1350- 1410) . Later the series was rediscovered and published in 1668 by James Gregory.
Compare with the series for sine, which is similar but has factorials in the denominator.
; the other, Exercitationes geometrica (Geometrical Exercises), at London
. He divided mathematics into "general" and "special" groups of theorems. He discovered the Taylor series
more than forty years before Brook Taylor
published it. The series for arctan x bears his name.
Series (mathematics)
A series is the sum of the terms of a sequence. Finite sequences and series have defined first and last terms, whereas infinite sequences and series continue indefinitely....
that was discovered by the Indian mathematician Madhava of Sangamagrama
Madhava of Sangamagrama
Mādhava of Sañgamāgrama was a prominent Kerala mathematician-astronomer from the town of Irińńālakkuţa near Cochin, Kerala, India. He is considered the founder of the Kerala School of Astronomy and Mathematics...
(1350- 1410) . Later the series was rediscovered and published in 1668 by James Gregory.
Definition
Gregory's series is defined as below:
Compare with the series for sine, which is similar but has factorials in the denominator.
History
In 1668 Gregory published two works. One of them, Geometriae pars universalis (The Universal Part of Geometry), was published in PaduaPadua
Padua is a city and comune in the Veneto, northern Italy. It is the capital of the province of Padua and the economic and communications hub of the area. Padua's population is 212,500 . The city is sometimes included, with Venice and Treviso, in the Padua-Treviso-Venice Metropolitan Area, having...
; the other, Exercitationes geometrica (Geometrical Exercises), at London
London
London is the capital city of :England and the :United Kingdom, the largest metropolitan area in the United Kingdom, and the largest urban zone in the European Union by most measures. Located on the River Thames, London has been a major settlement for two millennia, its history going back to its...
. He divided mathematics into "general" and "special" groups of theorems. He discovered the Taylor series
Taylor series
In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point....
more than forty years before Brook Taylor
Brook Taylor
Brook Taylor FRS was an English mathematician who is best known for Taylor's theorem and the Taylor series.- Life and work :...
published it. The series for arctan x bears his name.