泰勒级数简史

1712年,泰勒利用插值公式泰勒级数,但是没有讨论这一级数的收敛问题,因为当时很多数学家把级数看作是多项式的代数推广。以后欧拉、达朗具尔、高斯、柯西对级数理论、收敛性等进行了深入地讨论。

A SURVEY OF TAYLOR SERIES

In 1712 Brook Taylor derived a class of series, called Taylor series, by using an interpolation method. but he did not give any convergent properties of such kind of series, since then many mathematicians considered series as the algebric generalizations of polynomial. They found that the values of series can be finte and infinite, therfore it was necessary to study the convergence and divergence of series. In this short survery paper we review the origination of Taylor Serise and the thory of series. some works in this field of several great mathematisians, such as Newton, Taylor, Euler, D'-Alembere, Gauss, Lagrange and Cauchy, are discussed.