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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
HENG HUAT CHAN
Affiliation:
National University of Singapore, Department of Mathematics, Kent Ridge, Singapore 119260, Republic of Singapore
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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
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 124 , Issue 2 , September 1998 , pp. 193 - 204
Copyright
Cambridge Philosophical Society 1998

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Footnotes

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