RECURSIVE ALGORITHMS FOR NONNORMAL PADI TABLES*

realization problems is a special case of the Pad6 approximation problem. As a matter of fact, it computes among other polynomials the denominators of the elements of the Pad6 table that are on the descending diagonal {[0/1], [1/2], , [k/k + 1],.} as far as they exist and this algorithm works for nonnormal Pad6 tables too. This algorithm does not seem to be well-known in Pad6 approximation literature. It is not very difficult to generalize this algorithm so as to compute the other Pad6 approximants of a nonnormal table. Some variants will lead to a generalization of the algorithm of Brezinski [Computation ofPadd approximants continued fractions, J. Comput. Appl. Math., 2 (1976), pp. 113-123], which computes the descending diagonals of a normal Pad6 table, and of the algorithm of Watson [D. Bussonnais, "Tous " les algorithmes de calcul par recurrence des approximants de Padd d’une serie, Construction de fractions continuds cor-respondantes, S6minaire d’Analyse Num6rique, No. 293, Grenoble, 1978], [G. Claessens, A new look at the Pad # table and the different methods for computing its elements, J. Comput. Appl. Math., (1975), pp