- #1

- 2

- 0

## Homework Statement

Find the Taylor series expansion for f(x)=x*e^(-x^2) about x = -1

## Homework Equations

## The Attempt at a Solution

I have tried replacing x with (x-1) and f(x-1) = (x-1)*e^(-(x-1)^2).

Consider the power series for e^(-(x-1)^2) about x = 0, f(x-1) = (x-1)*(1/e+(2x-x^2)/e+(2x-x^2)^2/2!e+(2x-x^2)^3/3!e+...).

Let (x-1)*e^(-(x-1)^2) = A + Bx + Cx^2 + Dx^3 + Ex^4 + ...

So (x-1)*(1/e+(2x-x^2)/e+(2x-x^2)^2/2!e+(2x-x^2)^3/3!e+...) =A + Bx + Cx^2 + Dx^3 + Ex^4 + ...

Comparing x^n coefficients and I can get A, B,...

I don't know whether my method is correct and even it is correct ,it is too complicated.

I want an easier way to solve the problem.

Can anybody help me?

Thanks.