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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

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    Chan, Heng Huat Wan, James and Zudilin, Wadim 2012. Complex series for 1/π. The Ramanujan Journal, Vol. 29, Issue. 1-3, p. 135.

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    LIU, ZHI-GUO 2012. GAUSS SUMMATION AND RAMANUJAN-TYPE SERIES FOR 1/π. International Journal of Number Theory, Vol. 08, Issue. 02, p. 289.

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  • Heng Huat Chan (a1) (a2) and Wadim Zudilin (a3)
  • DOI:
  • Published online: 10 December 2009

We prove algebraic transformations for the generating series of three Apéry-like sequences. As application, we provide new binomial representations for the sequences. We also illustrate a method that derives three new series for 1/π from a classical Ramanujan’s series.

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[4]B. C. Berndt , H. H. Chan and S.-S. Huang , Incomplete elliptic integrals in Ramanujan’s lost notebook. Contemp. Math. 254 (2000), 79126.

[5]B. C. Berndt , H. H. Chan and W.-L. Liaw , On Ramanujan’s quartic theory of elliptic functions. J. Number Theory 88 (2001), 129156.

[7]H. H. Chan , S. H. Chan and Z. Liu , Domb’s numbers and Ramanujan–Sato type series for 1/π. Adv. Math. 186(2) (2004), 396410.

[8]H. H. Chan and H. Verrill , The Apéry numbers, the Almkvist–Zudilin numbers and new series for 1/π. Math. Res. Lett. 16(3) (2009), 405420.

[10]M. D. Rogers , New 5F4 hypergeometric transformations, three-variable Mahler measures, and formulas for 1/π. Ramanujan J. 18(3) (2009), 327340.

[12]W. Zudilin , Quadratic transformations and Guillera’s formulas for 1/π2. Math. Notes 81(3) (2007), 297301.

[13]W. Zudilin , Ramanujan-type formulae for 1/π: a second wind? In Modular Forms and String Duality (Banff, June 2006) (Fields Inst. Commun. 54) (ed. N. Yui), American Mathematical Society (Providence, RI, 2008), 179188.

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  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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