A new look at the Padé table and the different methods for computing its elements

AbstractIn this paper a survey is given of several algorithms for the computation of the Padé table of a formal power series. Those algorithms are studied which are based on certain relationships between adjacent elements in the Padé table. A new proof for the algorithms of Baker, Longman and for Gragg's variant of the qd-algorithm is given. A variant of Watson's algorithm is derived. The techniques used in this survey give some new ideas concerning the structure of the Padé table and the different ways to compute the elements of the table