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.
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Dedicated to the memory of Srinivasa Ramanujan
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Cooper, S. Sporadic sequences, modular forms and new series for 1/π . Ramanujan J 29, 163–183 (2012). https://doi.org/10.1007/s11139-011-9357-3
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DOI: https://doi.org/10.1007/s11139-011-9357-3