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RAMANUJAN'S CLASS INVARIANT λn AND A NEW CLASS OF SERIES FOR 1/π

Published online by Cambridge University Press:  24 August 2001

HENG HUAT CHAN ,
WEN-CHIN LIAW  and
VICTOR TAN
HENG HUAT CHAN
Affiliation:
Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 119260
WEN-CHIN LIAW
Affiliation:
Department of Mathematics, National Chung Cheng University, Chiayi 621, Taiwan
VICTOR TAN
Affiliation:
Department of Mathematics, National University of Singapore, Kent Ridge, Singapore 119260
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Abstract

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

Type
Research Article
Information
Journal of the London Mathematical Society , Volume 64 , Issue 1 , August 2001 , pp. 93 - 106
Copyright
The London Mathematical Society 2001

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