Approximants de Pade´ et se´ries hyperge´ome´triques e´quilibre´es

In this paper, we present and solve some very general new Pade´ approximant problems, whose solutions can be expressed with hypergeometric series. These series appear in the proofs of the irrationality of <f>ζ(3)</f>, of infinitely many <f>ζ(2n+1)</f>, and in essentially all results of this kind in the literature. We also prove two new Diophantine results with this method. [Copyright &y& Elsevier]