(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Using log taylor expansion to express cumulants in terms of moments

I have worked through the expansion- ##log(1+\epsilon)= ...## see thumbnail- and that's ok; my question is why does the expansion hold, i.e. all i can see is it must be that ##k## is small- how is this defined as so?

In all my studies on fourier transforms, I don't ever recall talking about the size of the transform variable being small- (minus the exception of perhaps a boundary condition, and then k is a function of L and then as L gets large k is small) but why here would we require k small, and why isn't this mentioned?

2. Relevant equations

my lectures notes here:

3. The attempt at a solution

as above

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# Statistical Mechanics- moments/cumulants, log expansion

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