Zeta function regularization

The zeta regularization 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.