Taylor series

In mathematical analysis, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the 18th century. Quotes Multiply the arc by the square of the arc, and take the result of repeating that [any number of times]. Divide [each of the above numerators] by the squares of successive even numbers increased by that number [lit. the root] and multiplied by the square of the radius. Place the arc and the successive results so obtained one below the other, and subtract each from the one above. These together give the jı̄vā, as collected together in the verse beginning with “vidvān” etc. Madhava of Sangamagrama (1340 CE), TantrasaṅgrahaVyākhyā/Yuktidı̄pikā An infinite series expansion for the sine and cosine (today called the “Taylor” series, after a pupil of Newton) was used by Madhava of Sangamagrama (1340 CE) to calculate precise sine and cosine values, by truncating the series to 11th and 12th order polynomials. The infinite series expansion is found in two verses stated in various texts, such as the TantrasaṅgrahaVyākhyā/Yuktidı̄pikā (2.440–443) (Sarma 1977). Sarma, K. V. (ed.), 1977, Tantrasaṅgraha of Nı̄lakan.t.ha Somayaji, with Yuktidı̄pikā and Laghuvivr.ti of Śaṅkara, VVBI, Panjab University, Hoshiarpur. quoted from Raju, C. K. ‘Calculus’. In Encyclopedia of Non-Western Science, Technology and Medicine, edited by Helaine Selin, 1010–15. Dordrecht: Springer, 2016. External links Category:Mathematics