英语翻译将函数展开成幂级数,从形式上看,但是由于幂级数的前项部分和是的多项式,而多项式是最简单的函数之一,因此用幂级数代替某个函数,实际上为函数的多项式逼近创造了条件.正是由

英语翻译将函数展开成幂级数,从形式上看,但是由于幂级数的前项部分和是的多项式,而多项式是最简单的函数之一,因此用幂级数代替某个函数,实际上为函数的多项式逼近创造了条件.正是由
英语翻译
将函数展开成幂级数,从形式上看,但是由于幂级数的前项部分和是的多项式,而多项式是最简单的函数之一,因此用幂级数代替某个函数,实际上为函数的多项式逼近创造了条件.正是由于这个原因,函数的幂级数展开式有着,广泛的应用.例如：对于函数值的近似计算、计算一些定积分的近似值.对于用幂级数近似计算函数值,其思路和以前学过的用微分近似公式或泰勒公式近似求值的思路相似.对于用幂级数近似计算定积分,特别是在某些被积函数的原函数不能用初等函数表示时,更显示出幂级数方法的优越性.最后应用复变量的指数函数的幂级数展开式,说明数学中重要的欧拉公式的形成与推导过程.
本文通过对幂级数的收敛范围的研究,以及通过对幂级数判别法的对比近一步了解幂级数,并熟悉针对特殊的情况下幂级数判别法的使用.

英语翻译将函数展开成幂级数,从形式上看,但是由于幂级数的前项部分和是的多项式,而多项式是最简单的函数之一,因此用幂级数代替某个函数,实际上为函数的多项式逼近创造了条件.正是由
Will function expansion into power series, from the form, as if the complicate the problem, but as referred to in the preceding paragraph shall be part of the power series and polynomial, and polynomial is one of the most simple function, therefore using power series instead of a function, actually create the conditions for the polynomial approximation function. It is for this reason, has a function of the power series expansion, a wide range of applications. For example: the function value of the definite integral approximate calculation, calculation of some approximation. For approximate calculation function value with a power series, the idea and before using differential approximation formula and Taylor formula approximate evaluation of similar ideas. With power series approximate calculation of definite integral, especially in some of the integrand function cannot be expressed in elementary function, more show the superiority of power series method. The application of the exponential function of complex variable, power series expansion of instructions in mathematics important formation and derivation of euler's formula.
In this paper, based on the research of the convergence range of the power series, and through comparison discriminant method of power series further understanding of power series, and familiar with for special cases, the use of the power series discriminant method.