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Quadratic transformations and Guillera’s formulas for 1/π2

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We prove two new series of Ramanujan type for 1/π2.

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References

  1. J. Guillera, “Some binomial series obtained by the WZ-method,” Adv. in Appl. Math. 29(4), 599–603 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  2. J. Guillera, “About a new kind of Ramanujan-type series,” Experiment. Math. 12(4), 507–510 (2003).

    MATH  MathSciNet  Google Scholar 

  3. J. Guillera, “Generators of some Ramanujan formulas,” Ramanujan J. 11(1), 41–48 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  4. J. Guillera, My Formulas for 1/π 2, Manuscript at http://personal.auna.com/jguillera/pi-formulas.pdf (2005).

  5. L. J. Slater, Generalized Hypergeometric Functions (Cambridge Univ. Press, Cambridge, 1966).

    MATH  Google Scholar 

  6. Y. Yang, “On differential equations satisfied by modular forms,” Math. Z. 246(1–2), 1–19 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  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), 396–410 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  8. Y. Yang (private communication, August 2005).

  9. G. Almkvist and W. Zudilin [V. V. Zudilin], “Differential equations, mirror maps and zeta values,” in Mirror Symmetry V, AMS/IP Stud. Adv. Math., Ed. by N. Yui, S.-T. Yau, and J. D. Lewis (Amer. Math. Soc. & International Press, Providence, RI, 2007), Vol. 38, pp. 481–515; arXiv: math.NT/0402386.

    Google Scholar 

  10. W. Zudilin [V. V. Zudilin], “Well-poised hypergeometric transformations of Euler-type multiple integrals,” J. London Math. Soc. (2) 70(1), 215–230 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  11. M. Petkovšek, H. S. Wilf, and D. Zeilberger, A = B (A. K. Peters, Ltd., Wellesley, MA, 1996).

    Google Scholar 

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Original Russian Text © V. V. Zudilin, 2007, published in Matematicheskie Zametki, 2007, Vol. 81, No. 3, pp. 335–340.

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Zudilin, V.V. Quadratic transformations and Guillera’s formulas for 1/π2 . Math Notes 81, 297–301 (2007). https://doi.org/10.1134/S0001434607030030

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  • DOI: https://doi.org/10.1134/S0001434607030030

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