Some Entries in Ramanujan’s Notebooks
نویسنده
چکیده
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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Ramanujan’s Earlier Notebooks and His Lost Notebook
Since the centenary of Ramanujan's birth, a large amount of Ramanujan's mathematics that had been ensconced in his earlier notebooks and in his lost notebook has been brought to light. In particular, in 1987, only one book had been written on Ramanujan's notebooks [2], but now several have appeared [2], [1]. We now have a larger portion of Ramanujan's mathematics to appreciate, evaluate, analyz...
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