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On Ramanujan's Quartic Theory of Elliptic Functions

✍ Scribed by Bruce C. Berndt; Heng Huat Chan; Wen-Chin Liaw

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
174 KB
Volume
88
Category
Article
ISSN
0022-314X

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✦ Synopsis

In his famous paper [11], [12, pp. 23 39], Ramanujan offers several elegant series for 1Γ‚?. He then remarks, ``There are corresponding theories in which q is replaced by one or other of the functions''

where r=3, 4, or 6 and where 2 F 1 denotes the classical Gaussian hypergeometric function. In the classical theory of elliptic functions, the variable

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