Summation of Series Defined by Counting Blocks of Digits
Jean-Paul Allouche, Jeffrey Shallit, Jonathan Sondow
Abstract
We discuss the summation of certain series defined by counting blocks of digits in the B-ary expansion of an integer. For example, if s2(n) denotes the sum of the base-2 digits of n, we show that Σn ≥ 1 s2(n)/(2n(2n+1)) = (γ+ 4π)/2. We recover this previous result of Sondow in math.NT/0508042 and provide several generalizations.
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