Help With Expansion of f(x) Function!

AI Thread Summary
The discussion revolves around expanding the function f(x) = exp(x)/(exp(x)-1)^2. The original poster seeks help with finding a series expansion for this function, expressing difficulty in understanding the process. Participants suggest methods such as computing the Taylor series and manipulating the function for easier expansion. The poster eventually recalls the Taylor series for exp(x) and successfully derives the needed expansion. The conversation highlights the importance of series expansions in calculus and problem-solving techniques.
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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
 
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What do you mean by expand? Do you mean just multiplying out the denominator?

f(x) = \frac{e^x}{e^{2x} - 2e^x + 1}
 
im just seing if there is a series expansion for the above, if not then it doesn't matter.
 
Of course there exists a series expansion of that function, why do you ask?
 
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.
 
Well, compute the first few terms of the Taylor series about some point, then! :smile:
 
How about adding and subtracting 1 from the numerator ?
 
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.
 
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
 
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