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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

New hypergeometric-like series for $ 1/\pi^2$ arising from Ramanujan's theory of elliptic functions to alternative base 3


Authors: Nayandeep Deka Baruah and Narayan Nayak
Journal: Trans. Amer. Math. Soc. 363 (2011), 887-900
MSC (2010): Primary 33C05; Secondary 33E05, 11F11, 11R29
Published electronically: August 24, 2010
MathSciNet review: 2728588
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Abstract: By using certain representations for Eisenstein series, we find new hypergeometric-like series for $ 1/\pi^2$ arising from Ramanujan's theory of elliptic functions to alternative base 3.


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Additional Information

Nayandeep Deka Baruah
Affiliation: Department of Mathematical Sciences, Tezpur University, Sonitpur, Pin-784028, India
Email: nayan@tezu.ernet.in

Narayan Nayak
Affiliation: Department of Mathematical Sciences, Tezpur University, Sonitpur, Pin-784028, India
Email: narayan.nayak05@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9947-2010-05180-3
PII: S 0002-9947(2010)05180-3
Keywords: Hypergeometric series, cubic theta functions, cubic modular equations, Eisenstein series
Received by editor(s): April 13, 2009
Published electronically: August 24, 2010
Dedicated: Dedicated to Professor Bruce C. Berndt on the occasion of his 70th birthday
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.