Derive the entire series expansion for the equation f(x)=(cos(x)/(1-x^2))

Question

loser66 · Answer

Are you dealing with generating function? or just regular derivative?

kainui · Answer

Just take the power series for cos(x) and then divide it by 1-x^2. =P

anonymous · Answer

I'm assuming that I need to generate a function

loser66 · Answer

@Kainui I don't think it is a piece of cake
let see, cos(x) = $\sum_{n=0}^\infty (-1)^n \dfrac{x^{2n}}{2n!}$
and $\dfrac{1}{1-x^2}=\sum_{n=0}^\infty x^{2n}$
combine them and then it becomes constant, if we take derivative, it is =0, not the right answer (I think)

loser66 · Answer

@Isaiah.Feynman  what do you think, it's cal2

loser66 · Answer

or discrete

loser66 · Answer

oh, derive, not derivative, oh!!! I am correct then, hehehe...

loser66 · Answer

I am sorry, I misread the stuff, it said "derive" not derivative. You can take my answer. :)

loser66 · Answer

why? you don't know how to expand the sum?

loser66 · Answer

waaat? I think you are at least in cal2 or discrete (which is high level of math) course. And you tell me that you don't know how to expand the sum ? hahahaha... you lie

anonymous · Answer

ha... well cal 2 I had taken like a few years ago, its differential equations.

loser66 · Answer

differential equation is 2 level higher than cal2. No way to believe that you don't know.