Zeta function regularization

In mathematics, zeta regularization is a summability method that allows one to give some meaningful values to seemingly meaningless expressions using the zeta function.

For example

${\displaystyle 1+2+3+\cdots =-{\frac {1}{12}}(\Re )}$

This infinite sum appears in the calculation of the Casimir force, and the regularized value of

${\displaystyle -{\frac {1}{12}}(\Re )}$

gives the correct physically measurable result.