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.
The importance of Taylor series is reflected in the following three aspects:
The derivation and integration of 1 and power series can be carried out item by item, so the summation function is easier.
2. Analytic function can be extended to Taylor series defined in the open domain on the complex plane, which is obtained by analytic continuation, making complex analysis possible.
3. Taylor series can be used to approximately calculate the function value.