Ramanujan's Lost Notebook - Andrews, George E.;Berndt, Bruce C.
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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." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony.
The "lost notebook" contains considerable material on mock theta functions and so undoubtedly emanates from the last year of Ramanujan's life. It…mehr

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Produktbeschreibung
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." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony.

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. Mathematicians are probably several decades away from a complete understanding of those functions. More than half of the material in the book is on q-series, including mock theta functions; the remaining part deals with theta function identities, modular equations, incomplete elliptic integrals ofthe first kind and other integrals of theta functions, Eisenstein series, particular values of theta functions, the Rogers-Ramanujan continued fraction, other q-continued fractions, other integrals, and parts of Hecke's theory of modular forms.
Autorenporträt
In the spring of 1976, George Andrews of Pennsylvania State University found "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. 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. Mathematicians are probably several decades away from a complete understanding of those functions.
Rezensionen
From the reviews: "The 'lost notebook' was in fact a 138-page manuscript found in materials from the estate of G.N. Watson. The manuscript, written in 'Ramanujan's distinctive handwriting', contained over 600 formulas. The authors have taken these results, provided proofs, placed them in the context of contemporary mathematics, and organized them accordingly ... This book is for the true fans of ... Ramanujan (Ramanuphiles?). If you enjoyed the original Ramanujan's Notebook series, then it's hard to pass this up." (Donald L. Vestal, MathDL-online, October 2006) "The present work is the first of an estimated four volumes devoted to all of the claims made by Ramanujan ... . The mathematics community owes a huge debt of gratitude to Andrews and Berndt for undertaking the monumental task of producing a coherent presentation along with complete proofs of the ... mathematical thoughts of Ramanujan during the last year of his life. ... Practitioners of q-series and other mathematicians interested in the work of Ramanujan, will delight in studying this book ... ." (Andrew V. Sills, Mathematical Reviews, Issue 2005 m)