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The Scientific World Journal
Volume 2014, Article ID 940358, 13 pages
Research Article

New Proofs of Some -Summation and -Transformation Formulas

Department of Mathematics, Chongqing Higher Education Mega Center, Chongqing Normal University, Huxi Campus, Chongqing 401331, China

Received 13 February 2014; Accepted 11 April 2014; Published 7 May 2014

Academic Editor: Kishin Sadarangani

Copyright © 2014 Xian-Fang Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We obtain an expectation formula and give the probabilistic proofs of some summation and transformation formulas of -series based on our expectation formula. Although these formulas in themselves are not the probability results, the proofs given are based on probabilistic concepts.