Ramanujan’s Notebooks

Part IV

Bruce C. Berndt (Autor)

Buch | Softcover

451 Seiten

2012 | Softcover reprint of the original 1st ed. 1994
Springer-Verlag New York Inc.
978-1-4612-6932-8 (ISBN)

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During the years 1903-1914, Ramanujan worked in almost complete isolation in India. During this time, he recorded most of his mathematical discoveries without proofs in notebooks. Although many of his results were already found in the literature, most were not. Almost a decade after Ramanujan's death in 1920, G.N. Watson and B.M. Wilson began to edit Ramanujan's notebooks, but they never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bombay in 1957. This book is the fourth of five volumes devoted to the editing of Ramanujan's notebooks. Parts I, II, and III, published in 1985, 1989, and 1991, contain accounts of Chapters 1-21 in Ramanujan's second notebook as well as a description of his quarterly reports. This is the first of two volumes devoted to proving the results found in the unorganized portions of the second notebook and in the third notebook. The author also proves those results in the first notebook that are not found in the second or third notebooks. For those results that are known, references in the literature are provided. Otherwise, complete proofs are given. Over 1/2 of the results in the notebooks are new. Many of them are so startling and different that there are no results akin to them in the literature.

22 Elementary Results.- 23 Number Theory.- 24 Ramanujan’s Theory of Prime Numbers.- 25 Theta-Functions and Modular Equations.- 26 Inversion Formulas for the Lemniscate and Allied Functions.- 27 q-Series.- 28 Integrals.- 29 Special Functions.- 30 Partial Fraction Expansions.- 31 Elementary and Miscellaneous Analysis.- Location in Notebook 2 of the Material in the 16 Chapters of Notebook 1>.- References.

Zusatzinfo	XII, 451 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
Schlagworte	Ramanujan
ISBN-10	1-4612-6932-6 / 1461269326
ISBN-13	978-1-4612-6932-8 / 9781461269328
Zustand	Neuware