Padé approximants are often better than Taylor series at representing a function. Given a Taylor series, one can use Wynn's epsilon algorithm to easily produce the Padé approximants to it.
Volterra series are a generalization of Taylor series that can also model "memory" phenomena. Does there exist a similar generalization of Padé approximants that can model these phenomena, or an algorithm like Wynn's to compute them from the Volterra series?