# taylor expansion

• February 18th 2009, 12:59 PM
tur
taylor 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
• February 18th 2009, 02:45 PM
Jester
Quote:

Originally Posted by tur
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

If you start with the Taylor series for $\tan x$

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

then you can integrate term by term.
• February 19th 2009, 04:20 AM
tur
thanks
Thanks a lot.

Lior