In this paper several examples belonging to different topics in Numerical Analysis are considered, making use of certain two-point Pad6 type Approximants with a single pole. Results about convergence and error estimations are given. 1. Theory Two-point Pad6 type approximants (in order to simplify the notation we shall write 2PTA's) were introduced by Draux [1] and Van Iseghem [2]. Recently, a formal study in the context of a noncommutative algebra has been made by Draux [3]. At the same time Gonz~lez-Vera [4] has carried out a treatment of these approximants in connection with Stieltjes series. Let us give the precise definition of a 2PTA according to Draux. Given two formal power series 00 00 f0= Ecj zj (zoO) and f~= Ec*j z-y, z ooo j=0 j=l and two nonnegative integers m and k (0 ~< k ~< m), if t)km is an arbitrary polynomial of degree m, then the rational function m-1 /m f~(z)=O~(z)/b~(z)= E ~,~'/ E b,z, j=0 /j=o where the coefficients { a i } are determined by imposing io-i,<m--O(z k) and i:-i~.~--O((z-,) '+') (l = m -k), is said to be a (k/m) two-point Pad6 type approximant to the pair (f0, f~), and we shall write fkm(Z) = (k/m)(fo, f~)(z ).
Let f(z) be a function analytic on neighbourhoods of z = 0 and z = ~, )Co and f~ being the