Mathematica evidence that Ramanujan kills Baker-Gammel-Wills

A 1961 conjecture of Baker, Gammel and Wills asserts that if a function f is meromorphic in the unit ball, and analytic at 0, then a subsequence of its diagonal Pade approximants converges uniformly in compact subsets omitting poles. Inasmuch as the denominators of the Padé approximants are complex orthogonal polynomials, and the convergence of sequences of Padé approximants is determined largely by the behaviour of their poles, the conjecture deals with distribution of zeros of complex orthogonal polynomials. In this paper, we present numerical evidence from the Mathematica package, that Ramanujan's continued fraction H q (z) = 1 + qzj j1 + q 2 zj j1 + q 3 zj j1 + ::: provides a counterexample, provided q is appropriately chosen on the unit circle.