On Ramanujan's cubic transformation formula for 2F1(1/3, 2/3; 1; z) 1
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)
1 This work is partially supported by NSF, grant number DMS-9304580.