# How would one do the following

by praharmitra
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 P: 311 How would one do the following sum? $$\sum\limits_{n=1}^\infty n e^{- \epsilon~n^2}$$
 Emeritus Sci Advisor HW Helper Thanks PF Gold P: 6,546 First of all, find out what epsilon is.
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 How would one do the following sum?
...carefully. What have you tried?

note $$\frac{d}{dn}e^{-\epsilon n^2}=-2\epsilon ne^{-\epsilon n^2}$$ ... may or may not be helpful.