AbstractIt is proved that the simple continued fractions for the irrational numbers defined by ∑k=0∞:U2k1 (u⩾3,an integer) and related quantities are predictable, that is, have a definite pattern. The proof uses only elementary properties of continued fractions. The nature of the partial quotients is discussed
AbstractLet An/Bn, n = 1,2,… denote the sequence of convergents of the nearest integer continued fra...
AbstractA new continued fraction algorithm is given and analyzed. It yields approximations for an ir...
AbstractWe use the continued fraction expansion ofαto obtain a simple, explicit formula for the sumC...
AbstractIn this paper we prove a theorem allowing us to determine the continued fraction expansion f...
Continued fractions in mathematics are mainly known due to the need for a more detailed presentation...
AbstractLet τ=[a0;a1,a2,…], a0∈N, an∈Z+, n∈Z+, be a simple continued fraction determined by an infin...
We consider the real number σ with continued fraction expansion [a0, a1, a2,...] = [1, 2, 1, 4, 1, ...
In this paper, we will first summarize known results concerning continued fractions. Then we will li...
AbstractFor any real number x, the continued fraction convergents pnqn to x form a sequence that is ...
There are numerous methods for rational approximation of real numbers. Continued fraction convergent...
AbstractWe investigate a one-parameter family of infinite generalised continued fractions. The fract...
AbstractThe continued fraction convergents to a random real number are shown to approximate that num...
AbstractA general theorem on correspondence of continued fractions to rational functions is proved. ...
AbstractLet {ai} with a1 ≥ 2 be an infinite bounded sequence of positive integers, and d1 = 1, di = ...
AbstractThe following conjecture of H.W. Lenstra is proved. Denote by pn/qn, n = 1,2,… the sequence ...
AbstractLet An/Bn, n = 1,2,… denote the sequence of convergents of the nearest integer continued fra...
AbstractA new continued fraction algorithm is given and analyzed. It yields approximations for an ir...
AbstractWe use the continued fraction expansion ofαto obtain a simple, explicit formula for the sumC...
AbstractIn this paper we prove a theorem allowing us to determine the continued fraction expansion f...
Continued fractions in mathematics are mainly known due to the need for a more detailed presentation...
AbstractLet τ=[a0;a1,a2,…], a0∈N, an∈Z+, n∈Z+, be a simple continued fraction determined by an infin...
We consider the real number σ with continued fraction expansion [a0, a1, a2,...] = [1, 2, 1, 4, 1, ...
In this paper, we will first summarize known results concerning continued fractions. Then we will li...
AbstractFor any real number x, the continued fraction convergents pnqn to x form a sequence that is ...
There are numerous methods for rational approximation of real numbers. Continued fraction convergent...
AbstractWe investigate a one-parameter family of infinite generalised continued fractions. The fract...
AbstractThe continued fraction convergents to a random real number are shown to approximate that num...
AbstractA general theorem on correspondence of continued fractions to rational functions is proved. ...
AbstractLet {ai} with a1 ≥ 2 be an infinite bounded sequence of positive integers, and d1 = 1, di = ...
AbstractThe following conjecture of H.W. Lenstra is proved. Denote by pn/qn, n = 1,2,… the sequence ...
AbstractLet An/Bn, n = 1,2,… denote the sequence of convergents of the nearest integer continued fra...
AbstractA new continued fraction algorithm is given and analyzed. It yields approximations for an ir...
AbstractWe use the continued fraction expansion ofαto obtain a simple, explicit formula for the sumC...
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