The Ramanujan Journal

August 2018, Volume 46, Issue 3, pp 667–675 | Cite as

Dougall’s \(_5F_4\) sum and the WZ algorithm

• Authors
• Authors and affiliations

• Jesús Guillera

Article

First Online: 16 April 2018

Received: 19 November 2016

Accepted: 19 January 2018

Abstract

We show how to prove the examples of a paper by Chu and Zhang using the WZ algorithm.

Keywords

Generalized hypergeometric series Dougall’s sum WZ algorithm Ramanujan-type series Evaluation of constants 

Mathematics Subject Classification

33C20 33F10 11Y60 

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References

1. 1.
   Chu, W., Zhang, W.: Accelerating Dougall’s \(_5F_4\)-sum and infinite series involving \(\pi \). Math. Comp. 83, 475–512 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
2. 2.
   Petkovs̆ek, M., Wilf, H., Zeilberger, D.: A = B. A.K. Peters Ltd., Wellesley (1996)Google Scholar
3. 3.
   Wilf, H., Zeilberger, D.: Rational functions certify combinatorial identities. J. Am. Math. Soc. 3(1), 147–158 (1990)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

• Jesús Guillera
  • 1
  Email author

1. 1.Department of MathematicsUniversity of ZaragozaZaragozaSpain