 On the other hand, if one uses stronger methods of summability, then the Dirichlet series for "η" defines a function on the whole complex plane — the Dirichlet eta function — and moreover, this function is analytic.For "z" with real part > −1 it suffices to use Cesàro summation, and so "η"(0) = 1⁄2 after all.The function "η" is related to a more famous Dirichlet series and function