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Math Help - ln (cos x) power series

  1. #1
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    ln (cos x) power series

    Is there a quick way to obtain the power series for ln(cos x) ?
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    Re: ln (cos x) power series

    Quote Originally Posted by Stuck Man View Post
    Is there a quick way to obtain the power series for ln(cos x) ?
    The simple answer is no.
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    Re: ln (cos x) power series

    How is it done?
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    Re: ln (cos x) power series

    FP2 - Maclaurin and Taylor Series - The Student Room

    What is the x in ln(1+x) that someone is talking about there?
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    Re: ln (cos x) power series

    Quote Originally Posted by Stuck Man View Post
    Is there a quick way to obtain the power series for ln(cos x) ?
    Yes there is, though you have to be a bit liberal with some absolute values. \displaystyle \begin{align*} \int{ -\tan{(x)}\,dx } = \ln{ \left| \cos{(x)} \right| } + C \end{align*}, so integrate the series for tan(x).
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    Re: ln (cos x) power series

    I had done it that way. Is the series valid for the same domain as the tan x series? That is -pi/2 < x < pi/2. I still don't understand the method used at The Student Room.
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