Question

e^(x^2+2x+1)关于(x+1)的幂级数展开式

Answer 1

e^x幂级数的展开式：

f(x)=e^x=x+x^2/2!+x^3/3!+...+x^n/n!

e^(x^2+2x+1)=e^[(x+1)^2]

=[(x+1)^2]+[(x+1)^2]^2/2!+[(x+1)^2]^3/3!+...+[(x+1)^2]^n/n!

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