can we use the tools of renormalization of casimir effect to get finite results for any divergent series in QFT?
for example let be the divergent series $ \sum_{n=1}^{\infty}n^{l} $ for positive 'l' then instead of the sum we interpretate this as the difference
$$ \sum_{n=1}^{\infty}n^{l}e^{-n\epsilon}-\int_{0}^{\infty}dtt^{l}e^{-t\epsilon}=finite$$
this is made to evaluate the infinite sums of the vaccuum energy in casimir effect but could it be done for any divergent series??
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