I have one question... In general I always thought that the exponential function was "dying" out faster than any other polynomial function, such that:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]e^{-x} x^a \rightarrow 0[/itex] for [itex]x \rightarrow \infty[/itex].

[eg this is was used quiet commonly and so I got it as a rule-of-thumb, when deriving wavefunctions for a simple example for the Hydrogen atom]

However recently I read in a paper that this is not true, and as an illustration of how can that be, they logarithm-ized the function like:

[itex]\ln (e^{-x} x^n) = -x + n \ln x[/itex] which goes to infinity for [itex] x,n\rightarrow \infty[/itex].

This I read in here:

http://arxiv.org/pdf/1108.4270v5.pdf

in Sec4 (the new paragraph after Eq4.1)

This has confused me, can someone shred some light?

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# I Does this go to 0 for large enough x?

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