Ramanujan's Lost Notebook: Part II

Hardcover | December 23, 2008

byGeorge E Andrews, Bruce C. Berndt

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In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated "Ramanujan's lost notebook." The "lost notebook" contains considerable material on mock theta functions and so undoubtedly emanates from the last year of Ramanujan's life. It should be emphasized that the material on mock theta functions is perhaps Ramanujan's deepest work.

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From the Publisher

In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated "Ramanujan's lost notebook." ...

From the Jacket

This volume is the second of approximately four volumes that the authors plan to write on Ramanujan's lost notebook, which is broadly interpreted to include all material published in The Lost Notebook and Other Unpublished Papers in 1988. The primary topics addressed in the authors' second volume on the lost notebook are q-series, Eise...

Format:HardcoverDimensions:432 pages, 9.25 × 6.1 × 0 inPublished:December 23, 2008Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387777652

ISBN - 13:9780387777658

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Extra Content

Table of Contents

Preface.- Introduction.- The Heine Transformation.- The Sears-Thomae Transformation.- Bilateral Series.- Well-poised Series.- Bailey's Lemma and Theta Expansions.- Partial Theta Functions.- Special Identities.- Theta Function Identities.- Ramanujan's Cubic Class Invariant.- Miscellaneous Results on Elliptic Functions and Theta Functions.- Formulas for the Power Series Cofficients of Certain Quotients of Eisenstein Series.- Letters From Matlock House.- Eisenstein Series and Modular Equations.- Series Representable in Terms of Eisenstein Series.- Eisenstein Series and Approximations to p.- Miscellaneous Results on Eisenstein Series.- Location Guide.- Provenance.- References.-

Editorial Reviews

From the reviews:"This volume contains 16 chapters comprising 314 entries. The material is arranged thematically with the main topics being some of Ramanujan's favorites q series theta functions . . the authors treatment is extremely thorough. Each chapter contains an introduction with appropriate background. References to all other known proofs of the entries are provided. . Fans of Ramanujan's mathematics are sure to be delighted by this book. . Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come." (Jeremy Lovejoy, Mathematical Reviews, Issue 2010 f)