Berndt Ramanujan

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Ramanujan’s Lost Notebook

neous sheets; and Ramanujan’s letters to G H Hardy written from nursing homes during Ramanujan’s ﬁnal two years in England This volume contains accounts of 442 entries (counting multiplicities) made by Ramanujan in the aforementioned publication The present authors have organized these claims

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Ramanujan’s lost notebook Part I

Apr 20 2006 · S 0273-0979(06)01110-4 Article electronically published on April 20 2006 Ramanujan’s lost notebook Part I by George E Andrews and Bruce C Berndt Springer New York 2005 xiv+437 pp US$89 95 ISBN 0-387-25529-X Ramanujan’s story is one of the great romantic tales of mathematics

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3 Ramanujan’s Notebooks

Sixty-seven years after the death of Ramanujan due to the discovery of the ‘lost’ notebook by Prof George Andrews in 1976 and the editing of the three Notebooks of Ramanujan by Prof Bruce Berndt there has been a resur-gence of interest in the work of Ramanujan These notebooks of Ramanujan

Did Ramanujan edit his notebooks?
Finally, in 1957 an unedited photostat edition of Ramanujan’s notebooks was published. This volume is the first of three volumes devoted to the editing of Ramanujan’s notebooks. Many of the results found herein are very well known, but many are new.
How did Bruce Berndt learn about Ramanujan?
Two years earlier, Bruce Berndt had learned of Ramanujan’s unpublished work on modular equations within the three original notebooks. In 1977, working from the Tata Institute’s facsimile publication of Ramanujan’s pre-1914 notebooks , he began the systematic study of the identities in chapter 14.
What is Ramanujan's generalization?
In his third notebook [227, p. 366] and on page 359 of his lost notebook , Ramanujan offers an extensive generalization of (10.3.1). This was first established independently by Berndt [62, pp. 269–273] and by R. McIntosh , who proved an even more general theorem by applying the Euler– Maclaurin summation formula in a skillful fashion.
Will Ramanujan's work be appreciated?
As stated elsewhere [XV], it is no exaggeration to say that as long as peo-ple do mathematics, the work of Ramanujan and the stupendous effort of Prof. Bruce C. Berndt in editing the Ramanujan notebooks will be appreci-ated. Prof. Ratan P. Agarwal is the founder of a school of ordinary and basic hy-pergeometric series in India.

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