= Zeta function regularization
= Zeta regularization
{synonym}
Zeta function regularization assigns a finite value to a divergent spectral sum by first forming a convergent complex-power series and then using its <analytic continuation>. For positive frequencies $\omega_n$, continue $\sum_n\omega_n^{-s}$ to $s=-1$ to define a regulated frequency sum, when that continuation is regular there. This does not turn the divergent positive-term sum into an ordinary convergent sum. It is a useful subtraction convention for the <normal-ordering constant of a string> and for vacuum energies.
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