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- W2952073362 abstract "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 earlier twentieth century. We show here that for carefully chosen $q$ on the unit circle, the Rogers-Ramanujan continued fraction $$1+frac{qz|}{|1}+frac{q^{2}z|}{|1}+frac{q^{3}z|}{|1}+... $$ provides a counterexample to the conjecture. We also highlight some other interesting phenomena displayed by this fraction." @default.
- W2952073362 created "2019-06-27" @default.
- W2952073362 creator A5014355369 @default.
- W2952073362 date "2004-02-18" @default.
- W2952073362 modified "2023-09-27" @default.
- W2952073362 title "Rogers-Ramanujan and the Baker-Gammel-Wills (Pad'e) conjecture" @default.
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