Mathematical Proceedings of the Cambridge Philosophical Society



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


HENG HUAT CHAN a1
a1 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.

(Received October 21 1996)
(Revised March 3 1997)



Footnotes

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