Results 21 to 30 of about 1,452,959 (130)
Convergence properties of the classical and generalized Rogers-Ramanujan continued fraction [PDF]
Research in Number Theory, 2015 The aim of this paper is to study the convergence and divergence of the Rogers-Ramanujan and the generalized Rogers-Ramanujan continued fractions on the unit circle.
Emil-Alexandru Ciolan, R. A. Neiss
exaly +2 more sources
Rational approximations to the Rogers-Ramanujan continued fraction [PDF]
Acta Arithmetica, 1988 Let \(f(\alpha,x)=1+\alpha x/(1+\alpha x^ 2/(1+\alpha x^ 3/(1+...]\) be the Rogers-Ramanujan continued fraction and let a, b, c, d be non-zero integers with \(| d| >c^ 2\). The following is proved: \(z=f(a/b,c/d)\) is an irrational number, and there exists a positive constant C depending on these integers only such that the inequality \(| z-p/q| \leq C/
I. Shiokawa
semanticscholar +3 more sources
The Rogers-Ramanujan continued fraction and a quintic iteration for 1/ [PDF]
Proceedings of the American Mathematical Society, 2007 Properties of the Rogers-Ramanujan continued fraction are used to obtain a formula for calculating 1/π with quintic convergence.
H. Chan, S. Cooper, Wen-Chin Liaw
semanticscholar +3 more sources
The Rogers–Ramanujan continued fraction and a new Eisenstein series identity☆
Journal of Number Theory, 2009 For complex \(\tau\) with \(\text{Im}(\tau)>0\), let \(q=e^{2\pi i\tau}\), and \[ G(z)=1+\sum_{n=1}^{\infty}\frac{q^{n^2}z^n}{(1-q)(1-q^2)\cdots(1-q^n)}. \] The relations \(G(1)=(q;q^5)_{\infty}^{-1}(q^4;q^5)_{\infty}^{-1}\) and \(G(q)=(q^2;q^5)_{\infty}^{-1}(q^3;q^5)_{\infty}^{-1}\) with \((a;q)_{\infty}=\prod_{n=1}^{\infty}(1-aq^n)\), are the well ...
H. Chan, S. Chan, Zhi-Guo Liu
semanticscholar +3 more sources
On relationships between q-products identities, Ralpha, Rbeta and Rm functions related to Jacobi's triple-product identity [PDF]
Mathematica Moravica, 2020 The authors establish a set of two new relationships involving q-product identities, Ralpha, Rbeta, and Rm (m = 1, 2, 3, . . .) functions; and answer a open question of Srivastava et al. [18].
Chaudhary M.P., Chaudhary Sangeeta
doaj +1 more source
Ramunujan's “Lost” Notebook III. The Rogers-Ramanujan continued fraction
Advances in Mathematics, 1981 G. Andrews
semanticscholar +2 more sources
The Reading Teacher, Volume 77, Issue 2, Page 189-198, September/October 2023., 2023 Abstract This article explores the potential of using children's literature in elementary mathematics classrooms as contexts for students to understand more fully the issues of equity, diversity, and inclusion. Informed by culturally responsive pedagogy, opportunities to link children's literature to mathematics education create cultural relevance for ...
Evan Throop Robinson
wiley +1 more source
Ramanujan’s function k(τ)=r(τ)r2(2τ) and its modularity
Open Mathematics, 2020 We study the modularity of Ramanujan’s function k(τ)=r(τ)r2(2τ)k(\tau )=r(\tau ){r}^{2}(2\tau ), where r(τ)r(\tau ) is the Rogers-Ramanujan continued fraction.
Lee Yoonjin, Park Yoon Kyung
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Golden Ratio and a Ramanujan-Type Integral
Axioms, 2013 In this paper, we give a pedagogical introduction to several beautiful formulas discovered by Ramanujan. Using these results, we evaluate a Ramanujan-type integral formula. The result can be expressed in terms of the Golden Ratio.
Hei-Chi Chan
doaj +1 more source
On relationships between q-product identities and combinatorial partition identities [PDF]
Mathematica Moravica, 2020 Andrews et al. [2] discussed about the combinatorial partition identities. We aim to present some relationships between q-product identities and combinatorial partition identities, by using and combining known formulas.
Chaudhary M.P. +2 more
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