ON RAMANUJANS CUBIC TRANSFORMATION FORMULA FOR F-2(1)(1 3,2/3,1,Z)/

Authors
CHAN HH
Citation
Hh. Chan, ON RAMANUJANS CUBIC TRANSFORMATION FORMULA FOR F-2(1)(1 3,2/3,1,Z)/, Mathematical proceedings of the Cambridge Philosophical Society, 124, 1998, pp. 193-204
Citations number
13
Categorie Soggetti
Mathematics,Mathematics
Journal title
Mathematical proceedings of the Cambridge Philosophical Society → ACNP
ISSN journal
03050041
Volume
124
Year of publication
1998
Part
2
Pages
193 - 204
Database
ISI
SICI code
0305-0041(1998)124:<193:ORCTFF>2.0.ZU;2-N
Abstract
The main aim of this paper is to provide two new proofs of Ramanujan's cubic transformation formula for F-2(1)(1/3, 2/3; 1; z) (see (1.8) be low). For our first proof, we have to develop Ramanujan's elliptic fun ctions in the theory of signature 3 using a different approach from th at given in a recent paper by Berndt, Bhargava and Garvan. For our sec ond proof, we use two of Goursat's formulas.