Results 21 to 30 of about 74,852 (243)
On the Generalized Rogers-Ramanujan Continued Fraction [PDF]
The Ramanujan Journal, 2003 The generalized Rogers-Ramanujan continued fraction is defined for \(| q|< 1\) and any complex \(a\) by \[ R(a,q)= {1\over 1}{\;\atop +} {aq\over 1}{\;\atop +} {aq^2\over 1}{\;\atop +} {aq^3\over 1}{\;\atop +}\cdots. \] The authors prove an asymptotic formula stated by Ramanujan for \(R(a,e^{-x})\) as \(x\to 0+\).
Berndt, Bruce C., Yee, Ae Ja
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Circuit complexity of knot states in Chern-Simons theory
Journal of High Energy Physics, 2019 We compute an upper bound on the circuit complexity of quantum states in 3d Chern-Simons theory corresponding to certain classes of knots. Specifically, we deal with states in the torus Hilbert space of Chern-Simons that are the knot complements on the 3-
Giancarlo Camilo +3 more
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A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales [PDF]
, 2018 A simple ansatz for the study of velocity autocorrelation functions in fluids at different timescales is proposed. The ansatz is based on an effective summation of the infinite continued fraction at a reasonable assumption about convergence of relaxation
Bryk, T. +2 more
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A New Algorithm to Approximate Bivariate Matrix Function via Newton-Thiele Type Formula
Journal of Applied Mathematics, 2013 A new method for computing the approximation of bivariate matrix function is introduced. It uses the construction of bivariate Newton-Thiele type matrix rational interpolants on a rectangular grid. The rational interpolant is of the form motivated by Tan
Rongrong Cui, Chuanqing Gu
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Ramanujan and the Regular Continued Fraction Expansion of Real Numbers [PDF]
, 2004 In some recent papers, the authors considered regular continued fractions of the form \[ [a_{0};\underbrace{a,...,a}_{m}, \underbrace{a^{2},...,a^{2}}_{m}, \underbrace{a^{3},...,a^{3}}_{m}, ...
Laughlin, James Mc, Wyshinski, Nancy J.
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Non-Equilibrium Liouville and Wigner Equations: Moment Methods and Long-Time Approximations
Entropy, 2014 We treat the non-equilibrium evolution of an open one-particle statistical system, subject to a potential and to an external “heat bath” (hb) with negligible dissipation.
Ramon F. Álvarez-Estrada
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A special case of rational θs for terminating θ-expansions [PDF]
Surveys in Mathematics and its Applications, 2013 There have been quite a few generalizations of the usual continued fraction expansions over the last few years. One very special generalization deals with θ-continued fraction expansions or simply θ-expansions introduced by Bhattacharya and Goswami [A ...
Santanu Chaktaborty
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Continued fractions, modular symbols, and non-commutative geometry [PDF]
, 2001 Using techniques introduced by D. Mayer, we prove an extension of the classical Gauss-Kuzmin theorem about the distribution of continued fractions, which in particular allows one to take into account some congruence properties of successive convergents ...
Manin, Yuri I., Marcolli, Matilde
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Fractal and FractionalThe paper deals with the problem of representing special functions by branched continued fractions, particularly multidimensional A- and J-fractions with independent variables, which are generalizations of associated continued fractions and Jacobi ...
Roman Dmytryshyn, Serhii Sharyn
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Generalized Continued Logarithms and Related Continued Fractions
, 2016 We study continued logarithms as introduced by Bill Gosper and studied by J. Borwein et. al.. After providing an overview of the type I and type II generalizations of binary continued logarithms introduced by Borwein et. al., we focus on a new generalization to an arbitrary integer base $b$.
Borwein, Jonathan M. +2 more
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