I am aware of the generalized Bernoulli numbers, but these are not what I'm looking for. I was wondering if there exists such a thing as fractional, real or even complex Bernoulli numbers ( $B_z$ for $z \in \mathbb{C}$).
My motivation comes from the Ramanujan Summation, as the Bernoulli numbers are involved in it. I was hoping that, if the Bernoulli numbers could be extendend, so could perhaps the Ramanujan Summation, allowing it to assign a sum to a wider class of divergent series.