George E. Andrews, Bruce C. Berndt

Ramanujan's Lost Notebook

Part I

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4419-2062-1
• Softcover reprint of hardcover 1st ed. 2005
• Seitenzahl: 452
• Erscheinungstermin: 30. September 2010
• Englisch
• Abmessung: 235mm x 155mm x 25mm
• Gewicht: 690g
• ISBN-13: 9781441920621
• ISBN-10: 1441920625
• Artikelnr.: 32213915

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.

Inhaltsangabe

Preface.- Introduction.- The 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)8/(q; q3)8.- 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.- Location Guide.- Provenance.- References.- Index.

Rezensionen

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)