Results 11 to 20 of about 795 (255)
Convergence criteria of branched continued fractions [PDF]
Researches in MathematicsThe convergence criteria of branched continued fractions with N branches of branching and branched continued fractions of the special form are analyzed.
I.B. Bilanyk, D.I. Bodnar, O.G. Vozniak
doaj +2 more sources
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
doaj +2 more sources
Applications of Hyperbolic Geometry to Continued Fractions and Diophantine Approximation [PDF]
, 2019 This dissertation explores relations between hyperbolic geometry and Diophantine approximation, with an emphasis on continued fractions over the Euclidean imaginary quadratic fields, Q(√−d), d = 1, 2, 3, 7, 11, and explicit examples of badly ...
Hines, Robert
core +8 more sources
Matrix-valued continued fractions [PDF]
, 2003 We discuss the properties of matrix-valued continued fractions based on Samelson inverse. We begin to establish a recurrence relation for the approximants of matrix-valued continued fractions.
Zhao, Huan-xi +3 more
core +1 more source
Continued Fraction Representations of the Generalized Operator Entropy
Tatra Mountains Mathematical Publications, 2023 Abstract The direct calculation of the generalized operator entropy proves to be difficult due to the appearance of rational exponents of matrices. The main motivation of this work is to overcome these difficulties and to present a practical and efficient method for this calculation using its representation by the matrix continued ...
Sarra Ahallal, Said Mennou, Ali Kacha
openaire +3 more sources
Hyperelliptic continued fractions and generalized Jacobians [PDF]
American Journal of Mathematics, 2019 For a complex polynomial $D(t)$ of even degree, one may define the continued fraction of $\sqrt{D(t)}$. This was found relevant already by Abel in 1826, and later by Chebyshev, concerning integration of (hyperelliptic) differentials; they realized that, contrary to the classical case of square roots of positive integers treated by Lagrange and Galois ...
openaire +3 more sources
Lattice Paths and Branched Continued Fractions: An Infinite Sequence of Generalizations of the Stieltjes-Rogers and Thron-Rogers Polynomials, with Coefficientwise Hankel-Total Positivity [PDF]
, 2023 We define an infinite sequence of generalizations, parametrized by an integer m ≥ 1, of the Stieltjes–Rogers and Thron–Rogers polynomials; they arise as the power-series expansions of some branched continued fractions, and as the generating polynomials
Zhu, B-X, Sokal, AD, Pétréolle, M
core +1 more source
Entropy, 2012 We consider non-equilibrium open statistical systems, subject to potentials and to external “heat baths” (hb) at thermal equilibrium at temperature T (either with ab initio dissipation or without it).
Ramon F. Alvarez-Estrada
doaj +1 more source
A generalization of continued fractions
Journal of Number Theory, 2011 Simple continued fractions are expressions of the form \(a_0+{1\over a_1+{\strut 1\over a_2+\cdots }}\), where \(a_i \in \mathbb{Z}\) and \(a_i \geq 1\) for \(i \geq 1\); the expansion may be finite or infinite. In this paper, the authors study what happens when the \(1\)'s in the numerators are replaced by a fixed but arbitrary positive integer \(N\).
Anselm, Maxwell, Weintraub, Steven H.
openaire +2 more sources
ARBITRARY ORDER RECURSIVE SEQUENCES AND ASSOCIATED CONTINUED FRACTIONS [PDF]
, 2017 The essential idea in this paper it to generalize and synthesize some of the pioneering ideas of Bernstein, Lucas and Horadam on generalizations of basic and primordial Fibonacci numbers and their arbitrary order generalizations and their relation to ...
Cook b, Charles K +2 more
core +1 more source