The Ramanujan Journal

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

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

  • Jesús Guillera


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


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

Mathematics Subject Classification

33C20 33F10 11Y60 


  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

  1. 1.Department of MathematicsUniversity of ZaragozaZaragozaSpain

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