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The Rogers–Ramanujan Identities and the Rogers–Ramanujan Continued Fraction
, 2017The Rogers–Ramanujan continued fraction is introduced, and two proofs of the Rogers–Ramanujan identifies are given.
M. Hirschhorn
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Convergence of the Rogers-Ramanujan continued fraction
Sbornik: Mathematics, 2003Set , where is an irrational number, and let be the radius of holomorphy of the Rogers-Ramanujan function As is known, and for each there exists such that . It is proved here that the function is meromorphic not only in the disc , but also in the disc , which is larger for ; and that the Rogers-Ramanujan continued fraction converges to on ...
V. Buslaev
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On the Rogers--Ramanujan Periodic Continued Fraction
Mathematical Notes, 2003In the paper, the convergence properties of the Rogers--Ramanujan continued fraction $$1 + \frac{qz}{1 + \tfrac{q^2 z}{1 + \cdots}}$$ are studied for q = exp (2 π i τ), where τ 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-
V I Buslaev, Buslaev V I
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On some continued fraction expansions of the Rogers–Ramanujan type
Ramanujan Journal, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Helmut Prodinger +2 more
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Explicit evaluations of the Rogers-Ramanujan continued fraction.
Journal für die reine und angewandte Mathematik (Crelles Journal), 1996L.-C. Zhang, H. Chan, B. C. Berndt
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About the Cover: The Continued Fraction of Rogers–Ramanujan
Computational Methods and Function Theory, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Level 5: The Rogers–Ramanujan Continued Fraction
2017We prove that $$\frac{q^{1/5}} {1 + \frac{q} {1+ \frac{q^{2}} {1+ \frac{q^{3}} {1+\cdots }}}} = q^{1/5}\prod _{ j=1}^{\infty }\frac{(1 - q^{5j-4})(1 - q^{5j-1})} {(1 - q^{5j-3})(1 - q^{5j-2})}$$ and develop the rich properties of the infinite product.
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A generalization of Shiokawa's rational approximations to the Rogers- Ramanujan continued fraction
Commentarii mathematici Universitatis Sancti Pauli = Rikkyo Daigaku sugaku zasshi, 1992Let \[ F=F(\alpha,\beta,x)= 1+{{\alpha x}\over {1+}} {{\beta x^ 2}\over {1+\dots}} {{\alpha x^{2n-1}} \over {1+}} {{\beta x^{2n}}\over {1+\dots}}. \] The following results are proved. Let \(a\), \(b\), \(c\), \(d\), \(f\) be integers \(\neq 0\) with \(| b^ 2 c^ 2 e^ 2|< | a^ 2 df^ 2|\), \(| a^ 2 c^ 2 f^ 2| Cq^{-2-2A-B/ \sqrt {(\log q)}} \tag ...
S., Bhargava +2 more
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