Thread: 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.

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

Not sure about the complex field, so I'll avoid replying ><

Originally Posted by Moo

Not sure about the complex field, so I'll avoid replying ><

It is okay for complex numbers too.
As long as you have one that is absolutely convergent.

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



where Writing out the first 8 or so derivatives, the odd and even derivatives repeat (outside of a factor of ), and when evaluated at , most vanish except every 4th derivative and the numbers turn out nice. Just an idea.