How to Generate All Possible Rational Wilf-Zeilberger Pairs?

  • Shaoshi ChenEmail author
Conference paper
Part of the Fields Institute Communications book series (FIC, volume 82)


A Wilf–Zeilberger pair (F, G) in the discrete case satisfies the equation
$$\displaystyle F(n+1, k) - F(n, k) = G(n, k+1) - G(n, k). $$
We present a structural description of all possible rational Wilf–Zeilberger pairs and their continuous and mixed analogues.



I would like to thank Prof. Victor J.W. Guo and Prof. Zhi-Wei Sun for many discussions on series for special constants, (super)-congruences and their q-analogues that can be proved using the WZ method. I am also very grateful to Ruyong Feng and Rong-Hua Wang for many constructive comments on the earlier version of this paper. I also thank the anonymous reviewers for their constructive and detailed comments.This work was supported by the NSFC grants 11501552, 11688101 and by the Frontier Key Project (QYZDJ-SSW-SYS022) and the Fund of the Youth Innovation Promotion Association, CAS.


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Authors and Affiliations

  1. 1.KLMM, Academy of Mathematics and Systems Science, Chinese Academy of SciencesBeijingChina
  2. 2.School of Mathematical SciencesUniversity of Chinese Academy of SciencesBeijingChina

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