Results 1 to 10 of about 48,907 (262)

Continued-Fraction Expansion of Transport Coefficients with Fractional Calculus [PDF]

Mathematics, 2016
The main objective of this paper is to generalize the Extended Irreversible Thermodynamics in order to include the anomalous transport in systems in non-equilibrium conditions.
Abel Garcia-Bernabé, S. I. Hernández, L. F. del Castillo, David Jou   +3 more
doaj   +7 more sources

Beta-expansion and continued fraction expansion

Journal of Mathematical Analysis and Applications, 2008
For a real number \(\beta > 1\), every real number \(x \in [0,1]\) has a \(\beta\)-expansion \(x = \sum_{n=1}^\infty \varepsilon_n(x) \beta^{-n}\). Such \(\beta\)-expansions in general are non-unique, but letting \(T_\beta x = \{\beta x\}\), where \(\{y\}\) denotes the fractional part of \(y\), we obtain such an expansion where \(\varepsilon_n(x ...
Li, Bing, Wu, Jun
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On the domains of convergence of the branched continued fraction expansion of ratio $H_4(a,d+1;c,d;\mathbf{z})/H_4(a,d+2;c,d+1;\mathbf{z})$

Researches in Mathematics, 2023
The paper considers the problem of establishing the convergence criteria of the branched continued fraction expansion of the ratio of Horn's hypergeometric functions $H_4$. To solve it, the technique of expanding the domain of convergence of the branched
R.I. Dmytryshyn, I.-A.V. Lutsiv, O.S. Bodnar   +2 more
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Prime numbers in typical continued fraction expansions

Bollettino dell'Unione Matematica Italiana, 2023
AbstractWe study, from the viewpoint of metrical number theory and (infinite) ergodic theory, the probabilistic laws governing the occurrence of prime numbers as digits in continued fraction expansions of real numbers.
Schindler, Tanja I., Zweimüller, Roland
openaire   +5 more sources

On the continued fraction expansions of $(1+\protect \sqrt{pq})/2$ and $\protect \sqrt{pq}$

Comptes Rendus. Mathématique, 2021
The evenness and the values modulo $4$ of the lengths of the periods of the continued fraction expansions of $\sqrt{p}$ and $\sqrt{2p}$ for $p\equiv 3\pmod {4}$ a prime are known.
Louboutin, Stéphane R.
doaj   +1 more source

Real numbers with polynomial continued fraction expansions [PDF]

Acta Arithmetica, 2005
In this paper we show how to apply various techniques and theorems (including Pincherle's theorem, an extension of Euler's formula equating infinite series and continued fractions, an extension of the corresponding transformation that equates infinite products and continued fractions, extensions and contractions of continued fractions and the Bauer ...
McLaughlin, James, Wyshinski, Nancy
openaire   +2 more sources

Representation of Some Ratios of Horn’s Hypergeometric Functions H₇ by Continued Fractions

Axioms, 2023
The paper deals with the problem of representation of Horn’s hypergeometric functions via continued fractions and branched continued fractions. We construct the formal continued fraction expansions for three ratios of Horn’s hypergeometric functions H7 ...
Tamara Antonova, Roman Dmytryshyn, Pavlo Kril, Serhii Sharyn   +3 more
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Some formulas related to Euler's product expansion for cosine function [PDF]

Notes on Number Theory and Discrete Mathematics
In this paper, we derive by using elementary methods some continued fractions, certain identities involving derivatives of tan x, several expressions for log cosh x and an identity for π², from a series expansion of tan x, which gives the product ...
Taekyun Kim, Dae San Kim
doaj   +1 more source

Some results on a special type of real quadratic fields

Қарағанды университетінің хабаршысы. Математика сериясы, 2019
In this paper, we determine the real quadratic fields Q(√d ) coincide with positive square - free integers d including the continued fraction expansion form of wd = [a0 ; 7,7,…,7 l-1 , al].
Ö. ¨Özer, D. Bellaouar
doaj   +1 more source

Approximation of functions of several variables by multidimensional $S$-fractions with independent variables

Karpatsʹkì Matematičnì Publìkacìï, 2021
The paper deals with the problem of approximation of functions of several variables by branched continued fractions. We study the correspondence between formal multiple power series and the so-called "multidimensional $S$-fraction with independent ...
R.I. Dmytryshyn, S.V. Sharyn
doaj   +1 more source