In mathematics, Taylor series is a series of infinite terms to represent a function, and these added terms are obtained by the derivative of the function at a certain point. Taylor series is named after British mathematician Brook Taylor, who published Taylor formula in 17 15.
Taylor series derived from the derivative of a function at the zero point of the independent variable is also called McLaughlin series, which is named after the Scottish mathematician colin maclaurin. Taylor series plays an important role in approximate calculation.
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The discovery history of Taylor series;
Greek philosopher Zhi Nuo? (Zhi Nuo of Elias) After considering the problem of getting finite results by summing infinite series, he came to an impossible conclusion-Zeno Paradox. Later Aristotle proposed a philosophical solution to Zeno's paradox, but obviously this part of mathematics was not solved until democritus and Archimedes took over. It is Archimedes' exhaustive method that subdivides an infinite series step by step and obtains limited results.
Enter14th century, Mā DH Ava of Sa&; Ntilde; Gamāgrama first used Taylor series and related methods. Although he did not keep work records, the later work of Indian mathematicians showed that he discovered some special Taylor series, including sine, cosine, tangent and arctangent trigonometric functions. After that, the school of astronomy and mathematics in Kerala made a series of extensions and reasonable approximations on his basis, which lasted until16th century.
In the17th century, James Gregory continued his research in this field and published several maclaurin series. Before 17 15, Brook Taylor proposed a general method to construct this order number, which is applicable to all functions. This is later known as Taylor series. Maclaurin series is named after maclaurin, a professor at Edinburgh University. He published a special case of Taylor series in18th century.