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Journal of the London Mathematical Society 2001 64(1):93-106; doi:10.1017/S0024610701002241
© 2001 by London Mathematical Society
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© The London Mathematical Society

Ramanujan's Class Invariant {lambda}n and a New Class of Series for 1/{pi}

Heng Huat Chan, Wen-Chin Liaw and Victor Tan

Department of Mathematics, National University of Singapore Kent Ridge, Singapore 119260
Department of Mathematics, National Chung Cheng University Chiayi 621, Taiwan

Received 21 February 2000. Revision received 8 September 2000.

On page 212 of his lost notebook, Ramanujan defined a new class invariant {lambda}n and constructed a table of values for {lambda}n. The paper constructs a new class of series for 1/{pi} associated with {lambda}n. The new method also yields a new proof of the Borweins' general series for 1/{pi} belonging to Ramanujan's ‘theory of q2’.


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