Thread: ln (cos x) power series

1. ln (cos x) power series

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

2. Re: ln (cos x) power series

Originally Posted by Stuck Man
Is there a quick way to obtain the power series for ln(cos x) ?

3. Re: ln (cos x) power series

How is it done?

4. 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?

5. Re: ln (cos x) power series

Originally Posted by Stuck Man
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 \displaystyle \begin{align*} \int{ -\tan{(x)}\,dx } = \ln{ \left| \cos{(x)} \right| } + C \end{align*}, so integrate the series for tan(x).

6. 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.