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Math Help - Taylor development

  1. #1
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    Taylor development

    Hey guys.
    I need to develop Taylor series for this function (cos(z) * cosh(z)).
    I know the Taylor development for cos and the Taylor development for cosh but I have no idea how to combine the two, if it's possible, any idea guys?
    And another thing, does it matters if we are talking about the complex field?

    Thanks a lot.
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  2. #2
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    Hello,
    Quote Originally Posted by asi123 View Post
    Hey guys.
    I need to develop Taylor series for this function (cos(z) * cosh(z)).
    I know the Taylor development for cos and the Taylor development for cosh but I have no idea how to combine the two, if it's possible, any idea guys?
    And another thing, does it matters if we are talking about the complex field?

    Thanks a lot.
    Cauchy product - Wikipedia, the free encyclopedia

    Not sure about the complex field, so I'll avoid replying ><
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    Quote Originally Posted by Moo View Post
    Not sure about the complex field, so I'll avoid replying ><
    It is okay for complex numbers too.
    As long as you have one that is absolutely convergent.
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  4. #4
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    Quote Originally Posted by asi123 View Post
    Hey guys.
    I need to develop Taylor series for this function (cos(z) * cosh(z)).
    I know the Taylor development for cos and the Taylor development for cosh but I have no idea how to combine the two, if it's possible, any idea guys?
    And another thing, does it matters if we are talking about the complex field?

    Thanks a lot.
    One might trying to expand the product but what I would try is a Taylor series

    \sum_{i=0}^{\infty} \frac{f^{(n)}(0)}{n!} z^n

    where f(z) = \cos z \cosh z. Writing out the first 8 or so derivatives, the odd and even derivatives repeat (outside of a factor of 2^p), and when evaluated at z = 0, most vanish except every 4th derivative and the numbers turn out nice. Just an idea.
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