Help With Expansion of f(x) Function!

[NEWO]

help! expansion

hi, I am trying to expand a function and can't seem to do it, if some one can tell me how to do it i would appreciate it trmendously. The following is the function;

f(x)=exp(x)/(exp(x)-1)^2

im guessing it is something simple, but i just can't grasp it.

Thank you for your time

newo

 

[berkeman]

What do you mean by expand? Do you mean just multiplying out the denominator?

$$f(x) = \frac{e^x}{e^{2x} - 2e^x + 1}$$

 

[NEWO]

im just seing if there is a series expansion for the above, if not then it doesn't matter.

 

[arildno]

Of course there exists a series expansion of that function, why do you ask?

 

[NEWO]

coz i need it, I can't find it!

by the way i have looked for it but my books are limited and I am not at uni at the mo so can't go to the library.

 

[arildno]

Well, compute the first few terms of the Taylor series about some point, then!

 

[arunbg]

How about adding and subtracting 1 from the numerator ?

 

[arildno]

Well, it might be simpler to write:
$$f(x)=\frac{d}{dx}\frac{1}{1-e^{x}}$$
and expand the denominator in the differentiand to the degree desired.

 

[NEWO]

its ok after looking through some stuff and asking my dad, lol I suddenly remembered about the taylor series of exp(x)=1+x+x^2/2! etc... and if x=c/a and if a>>c we can negate x^2 term due to being much smaller than the x term hence,

exp(x)---> 1+x

and I get what I needed anyway from that so that's great thanks anyway