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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.