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2014, Australian Mathematical Society lecture series, ISBN 0521186498, Volume 23, x, 212
Despite their classical nature, continued fractions are a neverending research area, with a body of results accessible enough to suit a wide audience, from researchers to students and even amateur enthusiasts... 
Processes, Infinite | Fractions | Continued fractions
Book
2006, ISBN 9812564772, xiii, 245
Book
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2016, Volume 443, Issue 2, pp. 1090 - 1094
In this paper, we provide some new continued fraction inequalities related to (1+1x)x. 
Multiple-correction | Approximations | Continued fraction
Journal Article
2008, Encyclopedia of mathematics and its applications, ISBN 0521854199, Volume 122, xvi, 478
Continued fractions, studied since Ancient Greece, only became a powerful tool in the eighteenth century, in the hands of the great mathematician Euler... 
Euler, Leonhard, 1707-1783 | Continued fractions | Orthogonal polynomials | Euler, Leonhard
Book
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 01/2020, Volume 89, Issue 321, pp. 351 - 372
We give a new class of multidimensional p-adic continued fraction algorithms. We propose an algorithm in the class for which we... 
MATHEMATICS, APPLIED | multidimensional p-adic continued fraction algorithms | Continued fractions
Journal Article
Applied Mathematics and Computation, ISSN 0096-3003, 06/2015, Volume 261, pp. 192 - 205
...). As applications, we establish a kind of hybrid-type finite continued fraction approximations related to BBP-type series of the constant π... 
BBP-type series | Rate of convergence | Multiple-correction | Catalan constant | Continued fraction | MATHEMATICS, APPLIED | SERIES | CONSTANT
Journal Article
Journal of Number Theory, ISSN 0022-314X, 07/2019, Volume 200, pp. 380 - 396
... and a parameter u, where the parameter b which defines the curve E5 is given as b=(ε5u5−ε−5)/(u5+1) and ε=(−1+5)/2. If r(τ) is the Rogers–Ramanujan continued fraction and b... 
Quintic equations | 5-division points | Rogers–Ramanujan continued fraction | Tate normal form | Watson's method | MATHEMATICS | FERMAT EQUATION | CLASS FIELDS | Rogers-Ramanujan continued fraction | PERIODIC POINTS | Mathematics - Number Theory
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2015, Volume 424, Issue 2, pp. 1425 - 1446
...]. As applications, we find a kind of hybrid-type finite continued fraction approximations in two cases of Landau constants and Lebesgue constants... 
Euler–Mascheroni constant | Landau constants | Rate of convergence | Multiple-correction | Lebesgue constants | Continued fraction | Euler-Mascheroni constant | MATHEMATICS, APPLIED | INEQUALITIES | SEQUENCES | MATHEMATICS | GOSPERS FORMULA | FOURIER-SERIES | GAMMA FUNCTION | CONVERGENCE | LEBESGUE
Journal Article
The Ramanujan Journal, ISSN 1382-4090, 6/2011, Volume 25, Issue 2, pp. 203 - 227
We derive two general transformations for certain basic hypergeometric series from the recurrence formulae for the partial numerators and denominators of two q-continued fractions previously investigated... 
q -series | Functions of a Complex Variable | Field Theory and Polynomials | Slater’s identities | 11A55 | Mathematics | Continued fractions | 33D15 | m -versions | Fourier Analysis | Rogers–Ramanujan identities | Number Theory | q -continued fraction | Combinatorics | m-versions | q-continued fraction | Slater's identities | q-series | Rogers-Ramanujan identities | MATHEMATICS | Mathematics - Number Theory
Journal Article
Nonlinearity, ISSN 0951-7715, 2017, Volume 30, Issue 3, pp. 1182 - 1203
We introduce a random dynamical system related to continued fraction expansions. It uses random combinations of the Gauss map and the Renyi (or backwards... 
random dynamical system | invariant measures | continued fractions | RANDOM BETA-TRANSFORMATION | MATHEMATICS, APPLIED | EXPANSIONS | PHYSICS, MATHEMATICAL | DIMENSIONS | INVARIANT-MEASURES | DENSITIES | NATURAL EXTENSIONS | DEPENDENT RANDOM MAPS | ENTROPY
Journal Article
Proceedings of the American Mathematical Society, ISSN 0002-9939, 05/2020, Volume 148, Issue 5, pp. 2111 - 2116
I give an elementary proof of Wall's continued-fraction characterization of Hausdorff moment sequences. 
Hausdorff moment sequence | MATHEMATICS | MATHEMATICS, APPLIED | binomial transform | continued fraction | Classical moment problem | Hamburger moment sequence | EULER | Stieltjes moment sequence
Journal Article
Encyclopedia of mathematics and its applications, Volume 11, xxviii, 428
Book
Advances in Mathematics, ISSN 0001-8708, 11/2016, Volume 303, pp. 295 - 321
Journal Article
Mathematics of Computation of the American Mathematical Society, ISSN 0025-5718, 11/2019, Volume 88, Issue 320, pp. 2913 - 2934
Multidimensional continued fractions (MCFs) were introduced by Jacobi and Perron in order to generalize the classical continued fractions... 
multidimensional continued fractions | p-adic numbers | MATHEMATICS, APPLIED | Jacobi-Perron algorithm | Continued fractions
Journal Article
Ergodic theory and dynamical systems, ISSN 0143-3857, 08/2018, Volume 38, Issue 5, pp. 1601 - 1626
... fraction algorithms PIERRE ARNOUX† and SÉBASTIEN LABBɇ † Equipe Groupes, Dynamique, Arithmétique et Combinatoire, Institut de Mathématique de Marseille, CNRS UMR... 
Original Article | MATHEMATICS | MATHEMATICS, APPLIED | GAUSS MEASURES | Invariants | Algorithms | Mathematics - Dynamical Systems | Dynamical Systems | Mathematics
Journal Article
Mathematische Zeitschrift, ISSN 0025-5874, 12/2017, Volume 287, Issue 3, pp. 1053 - 1064
We establish a new transcendence criterion of p-adic continued fractions which are called Ruban continued fractions... 
Diophantine approximations | Mathematics, general | Transcendental numbers | Mathematics | 11J81 | 11J70 | p -Adic numbers | 11J61 | Continued fractions | p-Adic numbers | MATHEMATICS | Mathematics - Number Theory
Journal Article
Rocky Mountain Journal of Mathematics, ISSN 0035-7596, 2018, Volume 48, Issue 1, pp. 219 - 236
In this paper, we introduce a generalization of palindromic continued fractions as studied by Adam-czewski and Bugeaud [2... 
Transcendental numbers | Continued fractions | transcendental numbers | MATHEMATICS | ALGEBRAIC-NUMBERS
Journal Article
Journal of number theory, ISSN 0022-314X, 2019, Volume 212, pp. 122 - 172
...) of quadratic numbers. We construct explicit upper and lower bounds on the period of the continued fraction expansion of a transformed number as a function of the period of the continued fraction expansion of the original number... 
Continued fraction period | Möbius transformation | Linear fractional transformation | Continued fraction | MATHEMATICS | LENGTH | SQUARE-ROOTS | Mobius transformation
Journal Article
Compositio mathematica, ISSN 0010-437X, 03/2018, Volume 154, Issue 3, pp. 565 - 593
We establish a combinatorial realization of continued fractions as quotients of cardinalities of sets... 
snake graphs | continued fractions | cluster algebras | MATHEMATICS | SNAKE GRAPH CALCULUS | POSITIVITY | CATEGORIES | SURFACES
Journal Article
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