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Math Help - Quadratic Taylor series

  1. #1
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    Exclamation Quadratic Taylor series

    I need to write a quadratic taylor series for the expression e^(-x^2). I have no clue. It was assumed that we could figure this one out for ourselves and I can't. Any help would be greatly appreciated!!
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by tulip View Post
    I need to write a quadratic taylor series for the expression e^(-x^2). I have no clue. It was assumed that we could figure this one out for ourselves and I can't. Any help would be greatly appreciated!!
    Centered around what?

    I will assume it is a zero.

    Since e^{x}=1+x+\frac{x^2}{2!}+...+\frac{x^n}{n!}=\sum_{  n=0}^{\infty}\frac{x^n}{n!}

    then e^{-x^2}=1-x^2+\frac{x^4}{2!}-...+\frac{(-x^2)^n}{n!}=\sum_{n=0}^{\infty}\frac{(-1)^nx^{2n}}{n!}

    There is the quadratic

    if you forget

    remember that the taylor series for f(x) centered around c is

    f(x)=f(c)+f'(c)(x-c)+\frac{f''(c)(x-c)^2}{2!}+...=\sum_{n=0}^{\infty}\frac{f^{(n)}(c)(  x-c)^n}{n!}

    assuming f(x) is analytic at x
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