Another observation on the distribution of values of continued fractions \(K(a_n/1)\)
It is known that the continued fractions \(K(a_n/1)\) takes limit values in the value region \(V=[-\rho,\rho]\) if the \(a_n\) are taken in the Worpitzky interval \(W=[-\rho(1-\rho),\rho(1-\rho)]\). \textit{L. Jacobsen}, \textit{W. J. Thron} and \textit{H. Waadeland} in [Numer. Math. 55, 711--733 (1989; Zbl 0704.40001)] and \textit{H. Waadeland} in [Probability distribution of continued fraction values. An invitation and an example, Commun. Anal. Theory Cont. Fractions 1, 40--45 (1992)] consider uniform distributions of the \(a_n\) in \(W\) and find the distribution of the limit values in \(V\). In this paper, the result is extended for distributions of \(a_n\) that are of the form \(b_0+b_1 | x| \). It turns out that also the limit values are distributed in a similar way with a slope that is greater than \(| b_1| \).
scientific article; zbMATH DE number 2060101