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

Processes, Infinite | Fractions | Continued fractions

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

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

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

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

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

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

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

9.
Full Text
Continued fraction proofs of m-versions of some identities of Rogers–Ramanujan–Slater type

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

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

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

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

The Hankel determinants of a given power series f can be evaluated by using the Jacobi continued fraction expansion of f...

Modulo p | Automatic proof | Stieltjes algorithm | Stern sequence | Integer sequence | Regular paperfolding sequence | Periodicity | Automatic sequence | Irrationality exponent | Hankel continued fraction | Hankel determinant | Thue–Morse sequence | Thue-Morse sequence | THUE-MORSE | MATHEMATICS | DETERMINANT CALCULUS | Combinatorics | Mathematics

Modulo p | Automatic proof | Stieltjes algorithm | Stern sequence | Integer sequence | Regular paperfolding sequence | Periodicity | Automatic sequence | Irrationality exponent | Hankel continued fraction | Hankel determinant | Thue–Morse sequence | Thue-Morse sequence | THUE-MORSE | MATHEMATICS | DETERMINANT CALCULUS | Combinatorics | Mathematics

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

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 LABBÉ‡ † 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

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

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

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

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

snake graphs | continued fractions | cluster algebras | MATHEMATICS | SNAKE GRAPH CALCULUS | POSITIVITY | CATEGORIES | SURFACES

Journal Article

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