The Ramanujan Journal

, Volume 29, Issue 1–3, pp 163–183 | Cite as

Sporadic sequences, modular forms and new series for 1/π

Article

Abstract

Two new sequences, which are analogues of six sporadic examples of D. Zagier, are presented. The connection with modular forms is established and some new series for 1/π are deduced. The experimental procedure that led to the discovery of these results is recounted. Proofs of the main identities will be given, and some congruence properties that appear to be satisfied by the sequences will be stated as conjectures.

Keywords

Congruence Modular form Pi Sporadic sequence 

Mathematics Subject Classification (2000)

11F11 11F27 11Y60 33C05 33E05 05A10 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Institute of Information and Mathematical SciencesMassey University-AlbanyAucklandNew Zealand

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