arXiv Open Access 2005

Summation of Series Defined by Counting Blocks of Digits

Jean-Paul Allouche Jeffrey Shallit Jonathan Sondow

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Abstrak

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 $\sum_{n \geq 1} s_2(n)/(2n(2n+1)) = (γ+ \log \frac{4}π)/2$. We recover this previous result of Sondow in math.NT/0508042 and provide several generalizations.

Topik & Kata Kunci

math.NT

Penulis (3)

Jean-Paul Allouche

Jeffrey Shallit

Jonathan Sondow

Format Sitasi

APA MLA BibTeX

Allouche, J., Shallit, J., Sondow, J. (2005). Summation of Series Defined by Counting Blocks of Digits. https://arxiv.org/abs/math/0512399

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Informasi Jurnal

Tahun Terbit: 2005
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓