[math-fun] Real index Bernoulli numbers?

Are there extensions of Bernoulli numbers to real (or complex) index? Is there one that is generally accepted as the natural way to do it? It would be nice if there were a natural real-index Bernoulli function that took real values. I read somewhere that Ramanujan used to refer to real order Bernoulli numbers in his notebooks. Does anyone know what definition he used? --Dan