Results 71 to 80 of about 1,452,959 (130)
Dynamics of a continued fraction of Ramanujan with random coefficients [PDF]
, 2005 We study a generalization of a continued fraction of Ramanujan with random, complex-valued 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, Jonathan M. Borwein
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Some Theorems on the Rogers-Ramanujan Continued Fraction in Ramanujan's Lost Notebook
, 2013 [[abstract]]In his first two letters to G. H. Hardy and in his notebooks, Ramanujan recorded many theorems about the Rogers-Ramanujan continued fraction. In his lost notebook, he offered several further assertions. The purpose of this paper is to provide
Berndt, Bruce C. ; Huang, Sen-Shan; Sohn, Jaebum; Son, Seung-Hwan
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Finite Rogers-Ramanujan type continued fractions
Journal of Algebra Combinatorics Discrete Structures and Applications, 2018 New finite continued fractions related to Bressoud and Santos polynomials are established.
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Analogue of Ramanujan\u27s function $k(τ)$ for the continued fraction $X(τ)$ of order six [PDF]
Motivated by the recent work of Park on the analogue of the Ramanujan\u27s function $k(τ)=r(τ)r^2(2τ)$ for the Ramanujan\u27s cubic continued fraction, where $r(τ)$ is the Rogers-Ramanujan continued fraction, we use the methods of Lee and Park to study ...
Guadalupe, Russelle +1 more
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Some Theorems On The Rogers-Ramanujan Continued Fraction In Ramanujan's Lost Notebook
. In his first two letters to G. H. Hardy and in his notebooks, Ramanujan recorded many theorems about the Rogers--Ramanujan continued fraction. In his lost notebook, he offered several further assertions.
Jaebum Sohn +3 more
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A note on a continued fraction of Ramanujan
, 2004 Ramanujan recorded many beautiful continued fractions in his notebooks. In this paper, we derive several identities involving the Ramanujan continued fraction c(q), including relations between c(q) and c(q(n)). We also obtain explicit evaluations of c(e(-
Adiga, Chandrashekar, Anitha, N.
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, 2019 In this part we show that the diophantine equation X5+Y5=ε5(1−X5Y5) , where ε=−1+5√2 , has solutions in specific abelian extensions of quadratic fields K=Q(−d−−−√) in which −d≡±1 (mod 5 ).
Morton, Patrick
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Explicit evaluations of the Rogers-Ramanujan continued fraction
In his first letter to G. H. Hardy, Ramanujan gave two explicit values for the Rogers-Ramanujan continued fraction \(F(q)\) and claimed that \(F(e^{-\pi \sqrt n})\) ``can be exactly found if \(n\) be any positive rational quantity.'' These two evaluations were established by G. N.
Berndt, B.C., Chan, H.H., Zhang, L.-C.
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RAMANUJAN’S CUBIC CONTINUED FRACTION AND RELATED RESULTS [PDF]
, 2015 On page 366 of his lost notebook [3], Ramanujan recorded a continued fraction known as Ramanujan’s Cubic Continued Fraction  defined as He also claimed that there are many results of  that are analogous to , Rogers-Ramanujan Continued Fraction.
Ojah, Kanan Kumari
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New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan's tau function. [PDF]
Proc Natl Acad Sci U S A, 1996 Milne SC.
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