27
Views
7
CrossRef citations to date
0
Altmetric
Original Article

A Class of Conjectured Series Representations for 1/π

Pages 409-414 | Published online: 30 Jan 2011

  • G. Almkvist and W. Zudilin. "Differential Equations, Mirror Maps and Zeta Values." To appear in Proceedings of the BIRS Workshop Calabi–Yau Varieties and Mirror Symmetry (Banff, December 6–11, 2003), edited by J. Lewis, S.-T. Yau, and N. Yui. Boston: International Press.
  • B. C. Berndt and H. H. Chan. "Eisenstein Series and Aproximation to π." Illinois Journal of Mathematics 45 (2001), 75–90.
  • J. M. Borwein, P. B. Borwein. Pi and the AGM. New York:Wiley-Interscience, 1987.
  • H. H. Chan. "Some New Identities Involving π, 1/π and 1/π2." Invited paper at the Asian Mathematical Conference 20–23 July 2005. Available online (http://ww1.math.nus.edu.sg/AMC/papers-invited/Chan-HengHuat.pdf), 2005. http://ww1.math.nus.edu.sg/AMC/papers-invited/Chan-HengHuat.pdf
  • H. H. Chan, W. C. Liaw, and V. Tan. "Ramanujan's Class Invariant λ n and a New Class of Series for 1/π." Journal of the London Mathematical Society 64 (2001), 93–106.
  • H.H.Chan, S. H. Chan, and Z. Liu. "Domb's Numbers and Ramanujan–Sato Type Series for 1/π." Advances in Mathematics 186 (2004), 396–410.
  • D. V. Chudnovsky and G. V. Chudnovsky. "Approximations and Complex Multiplication According to Ramanujan." In Ramanujan Revisited: Proceedings of the Centenary Conference, University of Illinois at Urbana–Champaign, June 1–5, 1987, edited by G. E. Andrews, B. C. Berndt, and R. A. Rankin, 375–472. Boston: Academic Press, 1987.
  • F. Garvan. "A q-Product Tutorial for a q- Series Maple Package." Available online (http://www. mat.univie.ac.at/~slc/wpapers/s42garvan.pdf), 2005. http://www.mat.univie.ac.at/~slc/wpapers/s42garvan.pdf
  • J. Guillera. "Generators of Some Ramanujan Formulas." Ramanujan Journal 11 (2006), 41–48.
  • J. Guillera. "A New Method to Obtain Series for 1/π and 1/π2." Experimental Mathematics 15:1 (2006), 83–89.
  • S. Ramanujan. "Modular Equations and Approximations to π." Quarterly Journal of Mathematics 45 (1914), 350–372.
  • T. Sato. "Apéry Numbers and Ramanujan's Series for 1/π." Abstract of a talk presented at the annual meeting of the Mathematical Society of Japan, March 28–31, 2002.
  • N. Sloane. "The On-Line Encyclopedia of Integer Sequences." Available online (http://www.research.att.com/~njas/sequences/), 2006. http://www.research.att.com/~njas/sequences/
  • Y. Yang. "On Differential Equations Satisfied by Modular Forms." Mathematische Zeitschrift 246 (2004), 1–19.
  • Y. Yang. Personal communication, 2005.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.