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|Title:||On Ramanujan's cubic transformation formula for 2F1 (1/3, 2/3; 1; z)|
|Source:||Chan, H.H. (1998-09). On Ramanujan's cubic transformation formula for 2F1 (1/3, 2/3; 1; z). Mathematical Proceedings of the Cambridge Philosophical Society 124 (2) : 193-204. ScholarBank@NUS Repository.|
|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. © 1998 Cambridge Philosophical Society.|
|Source Title:||Mathematical Proceedings of the Cambridge Philosophical Society|
|Appears in Collections:||Staff Publications|
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