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On Ramanujan's cubic transformation formula for 2F1(1/3, 2/3; 1; z)

Published online by Cambridge University Press:  01 September 1998

HENG HUAT CHAN
Affiliation:
National University of Singapore, Department of Mathematics, Kent Ridge, Singapore 119260, Republic of Singapore

Abstract

The main aim of this paper is to provide two new proofs of Ramanujan's cubic transformation formula for 2F1(1/3, 2/3; 1; z) (see (1·8) below). For our first proof, we have to develop Ramanujan's elliptic functions in the theory of signature 3 using a different approach from that given in a recent paper by Berndt, Bhargava and Garvan. For our second proof, we use two of Goursat's formulas.

Type
Research Article
Copyright
Cambridge Philosophical Society 1998

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Footnotes

This work is partially supported by NSF, grant number DMS-9304580.