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Ramanujan's Lost Notebook : Part I - George E. Andrews

Ramanujan's Lost Notebook

Part I

Paperback Published: 30th September 2010
ISBN: 9781441920621
Number Of Pages: 438

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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 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.

Industry Reviews

hematicians interested in the work of Ramanujan, will delight in studying this book ... ." (Andrew V. Sills, Mathematical Reviews, Issue 2005 m)

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.

ISBN: 9781441920621
ISBN-10: 1441920625
Audience: General
Format: Paperback
Language: English
Number Of Pages: 438
Published: 30th September 2010
Publisher: Springer-Verlag New York Inc.
Country of Publication: US
Dimensions (cm): 23.39 x 15.6  x 2.31
Weight (kg): 0.63

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