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Circular Summations of Theta Functions in Ramanujan's Lost Notebook

โœ Scribed by Seung Hwan Son


Book ID
111605970
Publisher
Springer US
Year
2004
Tongue
English
Weight
209 KB
Volume
8
Category
Article
ISSN
1382-4090

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On the Circular Summation of the Elevent
โœ Ken Ono ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 94 KB

Let f (a, b) denote Ramanujan's theta series. In his ``Lost Notebook'', Ramanujan claimed that the ``circular'' summation of n th powers of f satisfies a factorization of the form f (a n , b n ) F n (a n b n ) where F n (q)=1+2nq (n&1)ร‚2 + } } } . Moreover, he listed explicit closed formulas for F 2