Geodesic
On the Rogers--Ramanujan Periodic Continued Fraction
Matematičeskie zametki, Tome 74 (2003) no. 6, pp. 827-837.

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In the paper, the convergence properties of the Rogers–Ramanujan continued fraction $$ 1+\frac{qz}{1+\frac{q^2z}{1+\cdots}} $$ are studied for $q=\exp (2\pi i\tau)$, where $\tau$ is a rational number. It is shown that the function $H_q$ to which the fraction converges is a counterexample to the Stahl conjecture (the hyperelliptic version of the well-known Baker–Gammel–Wills conjecture). It is also shown that, for any rational $\tau$, the number of spurious poles of the diagonal Padé approximants of the hyperelliptic function $H_q$ does not exceed one half of its genus. 
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V. I. Buslaev; S. F. Buslaeva. On the Rogers--Ramanujan Periodic Continued Fraction. Matematičeskie zametki, Tome 74 (2003) no. 6, pp. 827-837. http://geodesic.mathdoc.fr/item/MZM_2003_74_6_a2/

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