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Ramanujan's Lost Notebook by George E. Andrews and Bruce C. Berndt (2005, Hardcover)
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Fundamentally Physics (1056)
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About this product
Product Identifiers
PublisherSpringer New York
ISBN-10038725529X
ISBN-139780387255293
eBay Product ID (ePID)15038263007
Product Key Features
Number of PagesXiv, 438 Pages
Publication NameRamanujan's Lost Notebook
LanguageEnglish
Publication Year2005
SubjectFunctional Analysis, Geometry / Algebraic, Mathematical Analysis
TypeTextbook
Subject AreaMathematics
AuthorGeorge E. Andrews, Bruce C. Berndt
FormatHardcover
Dimensions
Item Weight62.8 Oz
Item Length9.3 in
Item Width6.1 in
Additional Product Features
Intended AudienceScholarly & Professional
LCCN2005-923547
ReviewsFrom 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), From the reviews: "The a'lost notebooka? was in fact a 138-page manuscript found in materials from the estate of G.N. Watson. The manuscript, written in a?Ramanujana's distinctive handwritinga?, contained over 600 formulas. The authors have taken these results, provided proofs, placed them in the context of contemporary mathematics, and organized them accordingly a? This book is for the true fans of ... Ramanujan (Ramanuphiles?). If you enjoyed the original Ramanujana's Notebook series, then ita'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 a? . 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 a? mathematical thoughts of Ramanujan during the last year of his life. a? Practitioners of q-series and other mathematicians interested in the work of Ramanujan, will delight in studying this book a? ." (Andrew V. Sills, Mathematical Reviews, Issue 2005 m), hematicians interested in the work of Ramanujan, will delight in studying this book ... ." (Andrew V. Sills, Mathematical Reviews, Issue 2005 m), 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)
Dewey Edition22
Number of Volumes1 vol.
Volume NumberPt. 1
IllustratedYes
Dewey Decimal510
Table Of ContentInroduction.- Rogers-Ramanujan Continued Fraction and Its Modular Properties.- Explicit Evaluations of the Rogers-Ramanujan Continued Fraction.- A Fragment on the Rogers-Ramanujan and Cubic Continued Fractions.- The Rogers-Ramanujan Continued Fraction and Its Connections with Partitions and Lambert Series.- Finite Rogers-Ramanujan Continued Fractions.- Other q-continued Fractions.- Asymptotic Formulas for Continued Fractions.- Ramanujan's Continued Fraction for (q2;q3)?/(q;q3)?.- The Rogers-Fine Identity.- An Empirical Study of the Rogers-Ramanujan Identities.- Rogers-Ramanujan-Slater Type Identities.- Partial Fractions.- Hadamard Products for Two q-Series.- Integrals of Theta Functions.- Incomplete Elliptic Integrals.- Infinite Integrals of q-Products.- Modular Equations in Ramanujan's Lost Notebook.- Fragments on Lambert Series.
SynopsisIn 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., In the library at Trinity College, Cambridge in 1976, George Andrews of Pennsylvania State University discovered a sheaf of pages in the handwriting of Srinivasa Ramanujan. Soon designated "Ramanujan's lost notebook," it contains considerable material on mock theta functions and undoubtedly emanates from the last year of Ramanujan's life. Described as the mathematical equivalent of finding Beethoven's tenth symphony, the notebook is presented here with additional material and expert commentary., 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 of the 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., In the library at Trinity College, Cambridge in 1976, George Andrews of Pennsylvania State University discovered a sheaf of pages in the handwriting of Srinivasa Ramanujan. Soon designated as "Ramanujan's Lost Notebook," it contains considerable material on mock theta functions and undoubtedly dates from the last year of Ramanujan's life. In this book, the notebook is presented with additional material and expert commentary.
LC Classification NumberQA564-609
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