Geodesic
Rogers-Ramanujan and the Baker-Gammel-Wills (Padé) conjecture
Doron S. Lubinsky1
1 The John Knopfmacher Centre, University of Witwatersrand, Wits, South Africa , and School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, United States
Annals of mathematics, Tome 157 (2003) no. 3, pp. 847-889.

Voir la notice de l'article provenant de la source Annals of Mathematics website

In 1961, Baker, Gammel and Wills conjectured that for functions $f$ meromorphic in the unit ball, a subsequence of its diagonal Padé 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 Padé 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 \[ 1+\frac{qz|}{|1}+\frac{q^{2}z|}{|1}+\frac{q^{3}z|}{|1}+\cdots \] provides a counterexample to the conjecture. We also highlight some other interesting phenomena displayed by this fraction.
DOI : 10.4007/annals.2003.157.847

Doron S. Lubinsky 1

1 The John Knopfmacher Centre, University of Witwatersrand, Wits, South Africa , and School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332, United States 
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Doron S. Lubinsky. Rogers-Ramanujan and the Baker-Gammel-Wills (Padé) conjecture. Annals of mathematics, Tome 157 (2003) no. 3, pp. 847-889. doi : 10.4007/annals.2003.157.847. http://geodesic.mathdoc.fr/articles/10.4007/annals.2003.157.847/

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