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Rational analogues of Ramanujan's series for 1/π

Published online by Cambridge University Press:  17 May 2012

Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore117543. e-mail:
Institute of Information and Mathematical Sciences, Massey University-Albany, Private Bag 102904, North Shore Mail Centre, Auckland, New Zealand. e-mail:


A general theorem is stated that unifies 93 rational Ramanujan-type series for 1/π, 40 of which are believed to be new. Moreover, each series is shown to have a companion identity, thereby giving another 93 series, the majority of which are new.

Research Article
Copyright © Cambridge Philosophical Society 2012

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This work is supported by National University of Singapore Academic Research Fund R-146-000-103-112.


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Rational analogues of Ramanujan's series for 1/π
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