# Math Help - Taylor development

1. ## 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.

2. Hello,
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

3. Originally Posted by Moo
It is okay for complex numbers too.
As long as you have one that is absolutely convergent.

4. 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 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.