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Math Help - 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 \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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