منابع مشابه
Generalized Continued Logarithms and Related Continued Fractions
We study continued logarithms as introduced by Bill Gosper and studied by J. Borwein et. al.. After providing an overview of the type I and type II generalizations of binary continued logarithms introduced by Borwein et. al., we focus on a new generalization to an arbitrary integer base b. We show that all of our so-called type III continued logarithms converge and all rational numbers have fin...
متن کاملContinued Logarithms and Associated Continued Fractions
We investigate some of the connections between continued fractions and continued logarithms. We study the binary continued logarithms as introduced by Bill Gosper and explore two generalizations of the continued logarithm to base b. We show convergence for them using equivalent forms of their corresponding continued fractions. Through numerical experimentation we discover that, for one such for...
متن کاملPeriodic Continued Fractions And
We investigate when an algebraic function of the form φ(λ) = −B(λ)+ √ R(λ) A(λ) , where R(λ) is a polynomial of odd degree N = 2g + 1 with coefficients in C, can be written as a periodic α-fraction of the form
متن کاملPalindromic continued fractions
An old problem adressed by Khintchin [15] deals with the behaviour of the continued fraction expansion of algebraic real numbers of degree at least three. In particular, it is asked whether such numbers have or not arbitrarily large partial quotients in their continued fraction expansion. Although almost nothing has been proved yet in this direction, some more general speculations are due to La...
متن کاملContinued Fractions and Gaps
Given a continued fraction, we construct a certain function that is discontinuous at every rational number p/q. We call this discontinuity the “gap”. We then try to characterize the gap sizes, and find, to the first order, the size is 1/q2, and that, for higher orders, the gap appears to be perfectly ’randomly’ distributed, in that it is Cauchy-dense on the unit square, and thus, this function ...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1986
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1986-0813813-1