论文信息 - Summation of series defined by counting blocks of digits

Summation of series defined by counting blocks of digits

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 s 2 ( n ) denotes the sum of the base-2 digits of n , we show that ∑ n ⩾ 1 s 2 ( n ) / ( 2 n ( 2 n + 1 ) ) = ( γ + log 4 π ) / 2 . We recover this previous result of Sondow and provide several generalizations.

Jeffrey Shallit | Jean-Paul Allouche | Jonathan Sondow

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