Mathematica evidence that Ramanujan kills Baker-Gammel-Wills.
The famous Padé conjecture revised on 1961 by Baker, Gammel and Wills asserts that if a function \(f\) is meromorphic in the unit ball, and analytic at zero, then a subsequence of its diagonal Padé approximants converges uniformly in compact subsets omitting poles. Lubinsky and then Buslaev showed recently that this conjecture is false. In this paper the authors present numerical evidence derived using the Mathematica package, that \(f\) given by the Ramanujan continued fraction \(1+\frac{qz}{1+}\frac{q^2z}{1+}\frac{q^3z}{1+}\ldots\) provides a counterexample, provided \(q\) is appropriately chosen on the unit circle.
scientific article; zbMATH DE number 1861074
scientific article