# Taylor development

• January 27th 2009, 06:35 AM
asi123
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.
• January 27th 2009, 10:06 AM
Moo
Hello,
Quote:

Originally Posted by asi123
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

• January 27th 2009, 10:08 AM
ThePerfectHacker
Quote:

Originally Posted by Moo

It is okay for complex numbers too.
As long as you have one that is absolutely convergent.
• January 27th 2009, 11:08 AM
Jester
Quote:

Originally Posted by asi123
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 (Lipssealed) 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.