In zeta function regularization, the series formula_6 is replaced by the series formula_7. The latter series is an example of a Dirichlet series. When the real part of "s" is greater than 1, the Dirichlet series converges, and its sum is the Riemann zeta function "ζ"("s"). On the other hand, the Dirichlet series diverges when the real part of "s" is less than or equal to 1, so, in particular, the series that results from setting "s" = –1 does not converge. The benefit of introducing the Riemann zeta function is that it can be defined for other values of "s" by analytic continuation. One can then define the zeta-regularized sum of to be "ζ"(−1).