Results 11 to 20 of about 1,452,959 (130)
A full extension of the Rogers-Ramanujan continued fraction [PDF]
Proceedings of the American Mathematical Society, 1995 In this paper, we present the natural extension of the Rogers-Ramanujan continued fraction to the nonterminating very well-poised basic hypergeometric function
G. Andrews, D. Bowman
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On Diophantine Approximations of the Rogers-Ramanujan Continued Fraction
Journal of Number Theory, 1993 Sei \(F\) die durch \(F(t):= \sum_{k\geq 0} q^{k^ 2} t^ k/(1- q)\cdots (1- q^ k)\) definierte spezielle \(q\)-hypergeometrische Reihe; diese genügt der Funktionalgleichung \[ qt F(q^ 2 t)+ F(qt)= F(t). \tag{1}\] Mittels der klassischen Hurwitzschen Methode, die auf sukzessiver Iteration von (1) beruht, beweist Verf.
Tapani Matala-aho
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A birth and death process related to the Rogers-Ramanujan continued fraction [PDF]
Journal of Mathematical Analysis and Applications, 1998 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
P. R. Parthasarathy +3 more
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Some theorems on the explicit evaluation of Ramanujan's theta-functions
International Journal of Mathematics and Mathematical Sciences, 2004 Bruce C. Berndt et al. and Soon-Yi Kang have proved many of Ramanujan's formulas for the explicit evaluation of the Rogers-Ramanujan continued fraction and theta-functions in terms of Weber-Ramanujan class invariants.
Nayandeep Deka Baruah, P. Bhattacharyya
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Properties of reciprocity formulas for the Rogers–Ramanujan continued fractions [PDF]
Ramanujan Journal, 2019 Ramanujan recorded four reciprocity formulas for the Roger-Ramanujan continued fraction. Two reciprocity formulas each are also associated with the Ramanujan--Göllnitz--Gordon continued fraction and a level-13 analog of the Roger-Ramanujan continued fraction. We show that all eight reciprocity formulas are related to a pair of quadratic equations.
Rajeev Kohli
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The Rogers--Ramanujan continued fraction
The primary purpose of this paper is to provide a survey of properties, values, identities, and generalizations of the Rogers--Ramanujan continued fraction, which is closely related to the Rogers--Ramanujan identities.
Bruce C. Berndt, Ors Reb'ak
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On the Equivalence of Ramanujan's Partition Identities and a Connection with the Rogers)Ramanujan Continued Fraction [PDF]
, 1996 A famous identity of Ramanujan connected with partitions modulo 5 is shown to be equivalent to another identity of Ramanujan. The latter identity is used to establish a differential equation for the Rogers–Ramanujan continued fraction found in Ramanujan ...
H. Chan
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Identities for the Rogers-Ramanujan Continued Fraction [PDF]
We prove some new modular identities for the Rogers\textendash Ramanujan continued fraction. For example, if $R(q)$ denotes the Rogers\textendash Ramanujan continued fraction, then \begin{align*}&R(q)R(q^4)=\dfrac{R(q^5)+R(q^{20})-R(q^5)R(q^{20})}{1+R(q^{5})+R(q^{20})},\\ &\dfrac{1}{R(q^{2})R(q^{3})}+R(q^{2})R(q^{3})= 1+\dfrac{R(q)}{R(q^{6 ...
Baruah, Nayandeep Deka +1 more
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Tasoev's continued fractions and Rogers–Ramanujan continued fractions [PDF]
Journal of Number Theory, 2004 The author of this paper discusses Tasoev's continued fractions, which are of the form \[ [0;\underbrace{a,\dots,a}_m,\underbrace{a^2,\dots,a^2}_m, \dots]\equiv[0;\underbrace{\overline{a^k,\dots,a^k}}_m]_{k=1}^\infty,\;(m\geq1), \] and for a modified form he proves that \[ [0;\overline{ua^{2k-1}-1,1,va^{2k}-1}]_{k=1}^\infty=\frac{\sum_{s=0}^\infty u ...
Komatsu, Takao
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On the modified convergence of some continued fractions of Rogers-Ramanujan type [PDF]
Journal of Combinatorial Theory, Series A, 1994 In the analytic theory of continued fractions, the method of modified convergence is known for some time. This boils down to replacing the tail of a continued fraction by a fixed or variable number different from zero (that is what happens when a continued fraction is just `cut off').
University of Florida, Gainesville, Florida 32611 USA ( host institution ) +1 more
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