Rogers-Ramanujan and the Baker-Gammel-Wills (Padé) conjecture

By Doron S. Lubinsky. 2003

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In 1961, Baker, Gammel and Wills conjectured that for functions f meromorphic in the unit ball, a subsequence of its diagonal Pade approximants converges uniformly in compact subsets of the ball omitting poles of f. There is also apparently a cruder version of the conjecture due to Pade himself, going back to the early twentieth century. We show here that for carefully chosen q on the unit circle, the Rogers-Ramanujan continued fraction

Subfields: Algebra and Number Theory, Applied Mathematics

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