Results 141 to 150 of about 5,022,265 (207)

Continued Fractions

Exploring Continued Fractions, 2021
It is often necessary to approximate irrational numbers with rational ones. In music theory, for instance, we want the ratio of frequencies in moving an octave to be 2 and a fifth to be 3/2.
D. Angell
semanticscholar   +4 more sources

Continued fractions

Quadratic Number Theory, 2019
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.
A. Hernandez
semanticscholar   +3 more sources

Multifractal Analysis of the Convergence Exponent in Continued Fractions

Acta Mathematica Scientia, 2019
Let x ∈ (0, 1) be a real number with continued fraction expansion [a1 (x),a2 (x), a3(x), ⋯]. This paper is concerned with the multifractal spectrum of the convergence exponent of {an (x)}n≥1 defined by τ(x):=inf{s≥0:∑n≥1an−s(x)
Lulu Fang, Jihua Ma, Kunkun Song, Min Wu
semanticscholar   +1 more source

Noncommutative Continued Fractions

SIAM Journal on Mathematical Analysis, 1971
A number of theorems are proved concerning the convergence of continued fractions whose entries are linear operators on a Banach space. These theorems are analogues of some of the well-known results for ordinary continued fractions.
openaire   +1 more source

Popular products and continued fractions

Israel Journal of Mathematics, 2018
We prove bounds for the popularity of products of sets with weak additive structure, and use these bounds to prove results about continued fractions. Namely, considering Zaremba’s set modulo p , that is the set of all a such that $${a \over p} = [{a_1}, \
N. Moshchevitin, B. Murphy, I. Shkredov
semanticscholar   +1 more source

Generalized continued fractions

Applied Mathematics and Computation, 2000
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Ramanujan's Continued Fraction

Mathematical Proceedings of the Cambridge Philosophical Society, 1935
The best of the theorems on continued fractions, to be found in Ramanujan's manuscript note-book may be stated as follows:where there are eight gamma-functions in each product and the ambiguous signs are so chosen that the argument of each gamma-function contains one of the specified numbers of minus signs.
openaire   +2 more sources

Continued Fractions Continued, Applications

1989
We are now ready to explain the Brillhart-Morrison Continued Fraction Algorithm (commonly known as CFRAC) for factoring large numbers. The original idea is actually due to D. H. Lehmer and R. E. Powers in 1931 and it draws much of its inspiration from Legendre who used the continued fraction expansion in a procedure that restricted the congruence ...
openaire   +1 more source

Transcendental p-adic continued fractions

, 2014
We establish a new transcendence criterion of p-adic continued fractions which are called Ruban continued fractions. By this result, we give explicit transcendental Ruban continued fractions with bounded p-adic absolute value of partial quotients.
Tomohiro Ooto
semanticscholar   +1 more source

Metric properties of the product of consecutive partial quotients in continued fractions

Israel Journal of Mathematics, 2020
Lingling Huang, Jun Wu, Jian Xu
semanticscholar   +1 more source