20 citations · 82 across the 22 of their papers we have counts for
6 papers · 1 filter
On the Metrical Theory of a Generalized Continued Fraction Expansion
Dan Lascu, Katsunori Kawamura
We introduced a new continued fraction expansions in our previous paper. For these expansions, we show formulae of probability about incomplete quotients. Furthermore, we prove the…
Random Systems with Complete Connections and the Gauss Problem for the Regular Continued Fractions
Dan Lascu, Ion Coltescu
This paper present the important role that random system with complete connections played in solving the Gauss problem associated to the regular continued fractions. Hence, using t…
On the Szüsz's Solution to Gauss' Problem
Dan Lascu, Ion Coltescu
The present paper deals with Gauss' problem on continued fractions. We present a new proof of a theorem which Szüsz applied in order to solve this problem. To be noted, that we obt…
A New Type of Continued Fraction Expansion
Dan Lascu, Ion Coltescu
In this paper we define a new type of continued fraction expansion for a real number : \[x = \frac{m^{-b_1(x)}}{\displaystyle 1+\frac{m^{-b_2…
On a Gauss-Kuzmin Type Problem for a Family of Continued Fractions
Dan Lascu
We study a family of continued fraction expansion of reals from the unit interval. The Perron-Frobenius operator of the transformation which generates this expansion under the inva…
Properties of the nearest integer continued fraction expansions
Dan Lascu, George Cirlig, Ion Coltescu
The nearest integer continued fraction of a real number from is defined. Some metrical properties of these expansions are presented. We define the approximation c…