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Eisenstein series and Ramanujan-type series for 1/π

The Ramanujan Journal volume 23, pages 17–44 (2010)Cite this article

Abstract

Using certain representations for Eisenstein series, we uniformly derive several Ramanujan-type series for 1/π.

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam, India

    Nayandeep Deka Baruah

  2. Department of Mathematics, University of Illinois, 1409 West Green St., Urbana, IL, 61801, USA

    Bruce C. Berndt

Authors
  1. Nayandeep Deka Baruah
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  2. Bruce C. Berndt
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Corresponding author

Correspondence to Bruce C. Berndt.

Additional information

Dedicated to George Andrews on the occasion of his 70-th birthday

N.D. Baruah research partially supported by BOYSCAST Fellowship grant SR/BY/M-03/05 from DST, Govt. of India.

B.C. Berndt research partially supported by NSA grant MSPF-03IG-124.

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Baruah, N.D., Berndt, B.C. Eisenstein series and Ramanujan-type series for 1/π . Ramanujan J 23, 17–44 (2010). https://doi.org/10.1007/s11139-008-9155-8

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  • DOI: https://doi.org/10.1007/s11139-008-9155-8

Keywords

  • Eisenstein series
  • Theta-functions
  • Modular equations

Mathematics Subject Classification (2000)

  • 33C05
  • 33E05
  • 11F11
  • 11R29