A new family of Padé-type approximants in

AbstractThis paper gives the definition and some properties of a new family of Padé-type approximants (PTA) for k-variate formal power series (FPS). These PTA have the form P(t)/Q(t) where Q(t) = Πri = 0(1 − x(i)·t), {x(i), 0 ⩽ i ⩽ r} being a given set of points in , and x·t is the scalar product of x and t in . Some results about the approximation order, the unicity and some invariance properties of these PTA are proved together with a convergence result when the FPS is defined by a Stieltjes integral