|Journal of Integer Sequences, Vol. 14 (2011), Article 11.8.6|
Abstract: Let denote the -th convergent from the continued fraction expansion of some real number . We continue our work on error sum functions defined by and by proving a new density result for the values of and . Moreover, we study the function with respect to continuity and compute the integral . We also consider generalized error sum functions for the approximation with algebraic numbers of bounded degrees in the sense of Mahler.
(Concerned with sequences
Received May 13 2011; revised versions received July 12 2011; August 17 2011. Published in Journal of Integer Sequences, September 25 2011.