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Thread: taylor series expansion of exp^sinx

  1. #1
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    taylor series expansion of exp^sinx

    Hi,

    I need to expand e^sin(x)

    I have used the series for e^x and am trying to exapnd out the sin terms.

    I get

    1 + (x-....) + (1/2!)*(x-...)^2 + (1/3!)*(x-...)^3

    and want to simplify.

    Is 1 + x + (1/2!)*x^2 + (1/3!)*x^3 + ... the right simplification?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Roland25 View Post
    Hi,

    I need to expand e^sin(x)

    I have used the series for e^x and am trying to exapnd out the sin terms.

    I get

    1 + (x-....) + (1/2!)*(x-...)^2 + (1/3!)*(x-...)^3

    and want to simplify.

    Is 1 + x + (1/2!)*x^2 + (1/3!)*x^3 + ... the right simplification?
    If you are only interested in the first few terms rather than the general term, then you can use the definition of the Taylor series since $\displaystyle \exp(\sin(x))$ is easily differentiated a few times.

    CB
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  3. #3
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    I understand that, as thats one of the first things I did, but I'm after a simplified answer. I was just wondering if what I had writen was a feasible approximation or not when you expanded out the sin's
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