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46(th) Congress of The International Society of Paediatric Oncology (SIOP) 2014 Toronto, Canada, 22(nd) -25(th) October, 2014 SIOP Abstracts. [PDF]

Pediatr Blood Cancer, 2014
europepmc   +1 more source

Evaluations of the Rogers{Ramanujan continued fraction R(q) by modular equations

, 2001
Jinhee Yi
semanticscholar   +1 more source

Applications of the icosahedral equation for the Rogers-Ramanujan continued fraction

Let $R(q)$ denote the Rogers-Ramanujan continued fraction for $|q| < 1$. By applying the RootApproximant command in the Wolfram language to expressions involving the theta function $f(-q) := (q;q)_{\infty}$ given in modular relations due to Yi, this provides a systematic way of obtaining experimentally discovered evaluations for $R\big(e^{-π\sqrt{r}}
openaire   +2 more sources

On the Rogers-Ramanujan and Ramanujan-Gollnitz-Gordon Continued Fractions

94 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 1997.In a manuscript of Ramanujan, published with his Lost Notebook, there are forty identities involving the Rogers-Ramanujan functions. According to G. N.
Huang, Sen-Shan
core  

Dynamics of a continued fraction of Ramanujan with random coefficients

We study a generalization of a continued fraction of Ramanujan with random, complexvalued coefficients. A study of the continued fraction is equivalent to an analysis of the convergence of certain stochastic difference equations and the stability of ...
D. Russell Luke (21268967), Jonathan M. Borwein (21267920)   +1 more
core  

THE $w$-MODULAR FUNCTION AND THE EVALUATION OF ROGERS RAMANUJAN CONTINUED FRACTION

, 2013
N. Bagis
semanticscholar   +1 more source

О сходимости непрерывной дроби Роджерса - Рамануджана@@@Convergence of the Rogers - Ramanujan continued fraction

, 2003
Виктор Иванович Буслаев, V. I. Buslaev   +1 more
semanticscholar   +1 more source

On the Rogers-Ramanujan continued fraction [PDF]

Proceedings of the Indian Academy of Sciences - Section A, 1984
\textit{L. J. Rogers} [Proc. Lond. Math. Soc. 25, 318--343 (1894; JFM 25.0432.01)] and S. Ramanujan [see \textit{G. H. Hardy}, ``Ramanujan'' (1940; Zbl 0025.10505)] independently found that the continued fraction \(\frac{1}{1+}\frac{x}{1+}\frac{x^ 2}{1+}\cdots\) is equal to the ratio of theta functions \[ \prod (1-x^{5n-1})(1-x^{5n-4})/(1-x^{5n-2})(1 ...
K. G. Ramanathan
semanticscholar   +3 more sources

ON THE 1D AND 2D ROGERS–RAMANUJAN CONTINUED FRACTIONS [PDF]

Journal of Circuits, Systems and Computers, 2011
In this paper the classical and generalized numerical Rogers–Ramanujan continued fractions are extended to a polynomial continued fraction in one and two dimensions. Using the new continued fractions, the fundamental recurrence formulas and a fast algorithm, based on matrix formulations, are given for the computation of their transfer functions.
George E. Antoniou, Panagiota A. Katsalis   +1 more
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Sign patterns and congruences of certain infinite products involving the Rogers–Ramanujan continued fraction

Ramanujan Journal
We study the behavior of the signs of the coefficients of certain infinite products involving the Rogers–Ramanujan continued fraction. For example, if ∑n=0∞A(n)qn:=(q2;q5)∞5(q3;q5)∞5(q;q5)∞5(q4;q5)∞5,\documentclass[12pt]{minimal} \usepackage{amsmath ...
Baruah Nayandeep Deka, Abhishek Sarma
exaly   +2 more sources