- #1

fluidistic

Gold Member

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## Homework Statement

Hello guys, I fail to understand a mathematical approximation I see in a solved exercise.

The guy reached a partition function of ##Z=\sum_{l=0}^\infty (2l+1) \exp \left [ -l(l+1) \frac{\omicron}{T} \right ]## and he wants to analyze the case ##T>> \omicron##.

He states that with the change of variables ##x=l(l+1)\frac{\omicron}{T}##, ##Z\approx \frac{T}{\omicron} \int _0^\infty e^{-x}dx##.

I really don't understand this last step.

## Homework Equations

Sum becomes integral. The change of variables.

## The Attempt at a Solution

Making the change of variables, I understand that the sum transforms into an integral and I also understand why the limits of the integral are 0 and infinity (because l goes from 0 to infinity and thus x too).

I am unable to perform the change of variables and get rid of l's outside the exponential.

I'd appreciate if someone shed some light. Thanks.