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On Error Sum Functions Formed by Convergents of Real Numbers
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Carsten Elsner and Martin Stein

Fachhochschule für die Wirtschaft Hannover

Freundallee 15

30173 Hannover

Germany

**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.

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(Concerned with sequences
A000045
A007676
A007677
A041008
A041009.)

Received May 13 2011;
revised versions received July 12 2011; August 17 2011.
Published in *Journal of Integer Sequences*, September 25 2011.

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