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Journal of Difference Equations and Applications Volume 29, 2023 - Issue 3
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Research Article

Further WZ-based methods for proving and generalizing Ramanujan's series

John M. Campbella York University, Toronto, CanadaCorrespondence[email protected]
&
Paul Levrieb Faculty of Applied Engineering, UAntwerpen, Antwerp, Belgium;c Department of Computer Science, KU Leuven, Heverlee (Leuven), Belgium
Pages 366-376 | Received 07 Apr 2022, Accepted 26 Mar 2023, Published online: 12 Apr 2023

References

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  • J.M. Campbell, A WZ proof for a Ramanujan-like series involving cubed binomial coefficients, J. Differ. Equ. Appl. 27 (2021), pp. 1507–1511.
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  • S.B. Ekhad and D. Zeilberger, A WZ proof of Ramanujan's formula for π, in Geometry, Analysis and Mechanics, World Sci. Publ., River Edge, NJ, 1994, pp. 107–108
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  • Kh. Hessami Pilehrood and T. Hessami Pilehrood, Generating function identities for ζ(2n+2),ζ(2n+3) via the WZ method, Electron. J. Combin. 15 (2008), Research Paper 35, p. 9.
  • P. Levrie, Using Fourier-Legendre expansions to derive series for 1π and 1π2, Ramanujan J. 22 (2010), pp. 221–230.
  • P. Levrie and J. Campbell, Series acceleration formulas obtained from experimentally discovered hypergeometric recursions, Discrete Math. Theor. Comput. Sci. 24 (2023), Article ID Id/No 12.
  • P. Levrie and A.S. Nimbran, From Wallis and Forsyth to Ramanujan, Ramanujan J. 47 (2018), pp. 533–545.
  • OEIS Foundation Inc., The On-Line Encyclopedia of Integer Sequences, 2023; https://oeis.org.
  • M. Petkovšek, H.S. Wilf, and D. Zeilberger, A = B, A K Peters, Lts., Wellesley, MA, 1996.
  • S. Ramanujan, Modular equations and approximations to π, Q. J. Math. 45 (1914), pp. 350–372.
  • H.S. Wilf and D. Zeilberger, Rational functions certify combinatorial identities, J. Amer. Math. Soc.3 (1990), pp. 147–158.

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