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Some entries in Ramanujan's notebooks

Published online by Cambridge University Press:  01 March 2008

W. DUKE
W. DUKE*
Affiliation:
UCLA Mathematics Dept., Box 951555, Los Angeles, CA 90095, U.S.A. e-mail: wdduke@ucla.edu
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Extract

Some of Ramanujan's original discoveries about hypergeometric functions and their relation to modular integrals, especially Eisenstein series of negative weight, are still not very well understood. These discoveries take the form of identities that he recorded, without proof, as entries in his notebooks. In the following sections I will introduce some of these entries, discuss their status, give new proofs of several of them and also provide new results of a similar nature.

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Type
Research Article
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Mathematical Proceedings of the Cambridge Philosophical Society , Volume 144 , Issue 2 , March 2008 , pp. 255 - 266
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Copyright © Cambridge Philosophical Society 2008

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References

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