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Mat. Zametki, 2003, Volume 74, Issue 6, Pages 827–837 (Mi mz311)  

On the Rogers–Ramanujan Periodic Continued Fraction

V. I. Buslaeva, S. F. Buslaevab

a Steklov Mathematical Institute, Russian Academy of Sciences
b Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: 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.

DOI: https://doi.org/10.4213/mzm311

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English version:
Mathematical Notes, 2003, 74:6, 783–793

Bibliographic databases:

Received: 05.04.2003

Citation: V. I. Buslaev, S. F. Buslaeva, “On the Rogers–Ramanujan Periodic Continued Fraction”, Mat. Zametki, 74:6 (2003), 827–837; Math. Notes, 74:6 (2003), 783–793

Citation in format AMSBIB
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\transl
\jour Math. Notes
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\vol 74
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\pages 783--793
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