Results 71 to 80 of about 5,022,265 (207)

On the convergence criterion for branched continued fractions with independent variables

Karpatsʹkì Matematičnì Publìkacìï, 2018
In this paper, we consider the problem of convergence of an important type of multidimensional generalization of continued fractions, the branched continued fractions with independent variables.
R.I. Dmytryshyn
doaj   +1 more source

Palindromic continued fractions

, 2005
In the present work, we investigate real numbers whose sequence of partial quotients enjoys some combinatorial properties involving the notion of palindrome.
Adamczewski, Boris, Bugeaud, Yann
core   +3 more sources

Continued fractions built from convex sets and convex functions [PDF]

, 2014
In a partially ordered semigroup with the duality (or polarity) transform, it is possible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions with deterministic terms are provided.
I. Molchanov
semanticscholar   +1 more source

Probabilities as Values of Modular Forms and Continued Fractions

International Journal of Mathematics and Mathematical Sciences, 2009
We consider certain probability problems which are naturally related to integer partitions. We show that the corresponding probabilities are values of classical modular forms.
Riad Masri, Ken Ono
doaj   +1 more source

Hankel Determinants of Non-Zero Modulus Dixon Elliptic Functions via Quasi C Fractions

Fractal and Fractional, 2019
The Sumudu transform of the Dixon elliptic function with non-zero modulus α ≠ 0 for arbitrary powers N is given by the product of quasi C fractions.
Rathinavel Silambarasan, Adem Kılıçman   +1 more
doaj   +1 more source

Real number approximation by a rational number in the approximating k-ary algorithm

Учёные записки Казанского университета: Серия Физико-математические науки, 2019
The best approximation by the irreducible fraction with the denominator not exceeding some specified value n was investigated. The aim of this study was to find the fastest approximation algorithm that enables to accelerate the convergence of the k-ary ...
R.R. Enikeev
doaj   +1 more source

Continued fractions and Catalan problems

, 2000
We find a generating function expressed as a continued fraction that enumerates ordered trees by the number of vertices at different levels. Several Catalan problems are mapped to an ordered-tree problem and their generating functions also expressed as a
Jani, Mahendra, Rieper, Robert G.
core   +1 more source

Representation of Special Functions by Multidimensional A- and J-Fractions with Independent Variables

Fractal and Fractional
The 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   +1 more source

Convergence of Vectorial Continued Fractions Related to the Spectral Seminorm

Journal of Inequalities and Applications, 2008
We show that the spectral seminorm is useful to study convergence or divergence of vectorial continued fractions in Banach algebras because such convergence or divergence is related to a spectral property.
M. Amzil, M. Hemdaoui
doaj   +1 more source

The Continued Fraction Structure in Physical Fractal Theory

Fractal and Fractional
The objective of this study is to reveal the intrinsic connection between fractal operators in physical fractal spaces and continued fractions. The specific contributions include: (1) reviewing fundamental concepts of continued fractions and physical ...
Ruiheng Jiang, Tianyi Zhou, Yajun Yin
doaj   +1 more source