Advertisement

aequationes mathematicae

, Volume 70, Issue 1–2, pp 25–36 | Cite as

Evaluations of binomial series

  • Jonathan M. BorweinEmail author
  • Roland Girgensohn
Research paper

Summary.

We give closed forms, recursion formulas and experimental results for the series \({\sum {{n^{k} } \mathord{\left/ {\vphantom {{n^{k} } {{\left( {\begin{array}{*{20}c} {{2n}} \\ {n} \\ \end{array} } \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {\begin{array}{*{20}c} {{2n}} \\ {n} \\ \end{array} } \right)}}}}\) and \({\sum {{2^{{ - n}} n^{k} } \mathord{\left/ {\vphantom {{2^{{ - n}} n^{k} } {{\left( {\begin{array}{*{20}c} {{3n}} \\ {n} \\ \end{array} } \right)}}}} \right. \kern-\nulldelimiterspace} {{\left( {\begin{array}{*{20}c} {{3n}} \\ {n} \\ \end{array} } \right)}}} }\;\hbox{with}\;k\,\in\,\mathbb{Z}.\)

Mathematics Subject Classification (2000).

Primary 05A10 11B65 Secondary 11Y16 11Y65 

Keywords.

Binomial coefficients Polylogarithms Lehmer’s sums Integer relation algorithms 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Faculty of Computer ScienceDalhousie UniversityHalifaxCanada
  2. 2.Zentrum MathematikTechnische Universität MünchenMünchenGermany

Personalised recommendations