Duality in Padé-type approximation

摘要

Padé and Padé-type approximants are usually defined by replacing the function (1 − xt)−1 by its Hermite (that is confluent) interpolation polynomial and then applying the functional c defined by c(xi) = ci where the ci's are the coefficients of the series to be approximated. In this paper the functional d which, applied to (1 − xt)−1, gives the same Padé or Padé-type approximant as before is studied. It can be considered as the dual of the interpolation operator applied to the functional c.