求函数f(x)=e^(-x^2)在x1=o处的n+1阶泰勒展开式_数学解答

求函数f(x)=e^(-x^2)在x1=o处的n+1阶泰勒展开式

人气：300 ℃　时间：2019-10-17 06:36:43

解答

e^x=1+x+x^2/2!+x^3/3!+...+x^(n+1)/(n+1)!+o(x^(n+1))
e^(-x^2)=1-x^2+x^4/2!-x^6/3!+...+(-1)^(n)x^(2n+2)/(n+1)!+o(x^(2n+3))