Hi to all,

I'm trying to find a general formula for the taylor expansion around 0 of

ln(cos(x))

I know how to get the first terms yet no general formula for the series that i get

does anyone know how to do it?

Thanks, Lior

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- Feb 18th 2009, 12:59 PMturtaylor expansion
Hi to all,

I'm trying to find a general formula for the taylor expansion around 0 of

ln(cos(x))

I know how to get the first terms yet no general formula for the series that i get

does anyone know how to do it?

Thanks, Lior - Feb 18th 2009, 02:45 PMJester
If you start with the Taylor series for $\displaystyle \tan x$

$\displaystyle \sum_{n=1}^{\infty}B_{2n} \frac{(-4)^n \left( 1 - 4^n\right)}{(2n)!}\, x^{2n-1}$ where $\displaystyle B_{2n}$ are the Bernoulli numbers (see Taylor series - Wikipedia, the free encyclopedia)

then you can integrate term by term. - Feb 19th 2009, 04:20 AMturthanks
Thanks a lot.

Lior