Ramanujan’s Notebooks de Bruce C. Berndt

Ramanujan’s Notebooks: Part V

Bruce C. Berndt

The fifth and final volume to establish the results claimed by the great Indian mathematician Srinivasa Ramanujan in his "Notebooks" first published in 1957. Although each of the five volumes contains many deep results, the average depth in this volume is possibly greater than in the first four. There are several results on continued fractions - a subject that Ramanujan loved very much. It is the authors wish that this and previous volumes will serve as springboards for further investigations by mathematicians intrigued by Ramanujans remarkable ideas.

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	Preț	Express
Paperback (5)	987^.49 lei 6-8 săpt.
Springer – 26 sep 2011	987^.49 lei 6-8 săpt.
Springer – 30 sep 2012	1099^.26 lei 6-8 săpt.
Springer – 2 oct 2012	1201^.43 lei 6-8 săpt.
Springer – 30 sep 2012	1530^.56 lei 6-8 săpt.
Springer – 27 oct 2012	1536^.45 lei 6-8 săpt.
Hardback (5)	1020^.84 lei 6-8 săpt.
Springer – 18 ian 1999	1020^.84 lei 6-8 săpt.
Springer – 17 dec 1993	1137^.50 lei 6-8 săpt.
Springer – 12 mar 1985	1234^.65 lei 6-8 săpt.
Springer – 9 ian 1997	1571^.91 lei 6-8 săpt.
Springer – 12 dec 1997	1584^.23 lei 6-8 săpt.

Preț

Express

Paperback (5)

987^.49 lei 6-8 săpt.

Springer – 26 sep 2011

987^.49 lei 6-8 săpt.

Springer – 30 sep 2012

1099^.26 lei 6-8 săpt.

Springer – 2 oct 2012

1201^.43 lei 6-8 săpt.

Springer – 30 sep 2012

1530^.56 lei 6-8 săpt.

Springer – 27 oct 2012

1536^.45 lei 6-8 săpt.

Hardback (5)

1020^.84 lei 6-8 săpt.

Springer – 18 ian 1999

1020^.84 lei 6-8 săpt.

Springer – 17 dec 1993

1137^.50 lei 6-8 săpt.

Springer – 12 mar 1985

1234^.65 lei 6-8 săpt.

Springer – 9 ian 1997

1571^.91 lei 6-8 săpt.

Springer – 12 dec 1997

1584^.23 lei 6-8 săpt.

Descriere

During the years 1903-1914, Ramanujan recorded most of his mathematical dis coveries without proofs in notebooks. Although many of his results had already been published by others, most had not. Almost a decade after Ramanujan's death in 1920, G. N. Watson and B. M. Wilson began to edit Ramanujan's notebooks, but, despite devoting over ten years to this project, they never completed their task. An unedited photostat edition of the notebooks was published by the Tata Institute of Fundamental Research in Bombay in 1957. This book is the fifth and final volume devoted to the editing of Ramanujan's notebooks. Parts I-III, published, respectively, in 1985, 1989, and 1991, contain accounts of Chapters 1-21 in the second notebook, a revised enlarged edition of the first. Part IV, published in 1994, contains results from the 100 unorganized pages in the second notebook and the 33 unorganized pages comprising the third notebook. Also examined in Part IV are the 16 organized chapters in the first notebook, which contain very little that is not found in the second notebook. In this fifth volume, we examine the remaining contents from the 133 unorganized pages in the second and third notebooks, and the claims in the 198 unorganized pages of the first notebook that cannot be found in the succeeding notebooks.

Cuprins

32 Continued Fractions.- 1 The Rogers—Ramanujan Continued Fraction.- 2 Other q—Continued Fractions.- 3 Continued Fractions Arising from Products of Gamma Functions.- 4 Other Continued Fractions.- 5 General Theorems.- 33 Ramanujan’s Theories of Elliptic Functions to Alternative Bases.- 1 Introduction.- 2 Ramanujan’s Cubic Transformation, the Borweins’ Cubic Theta—Function Identity, and the Inversion Formula.- 3 The Principles of Triplication and Trimidiation.- 4 The Eisenstein Series L, M, and N.- 5 A Hypergeometric Transformation and Associated Transfer Principle.- 6 More Higher Order Transformations for Hypergeometric Series.- 7 Modular Equations in the Theory of Signature 3.- 8 The Inversion of an Analogue of K (k) in Signature 3.- 9 The Theory for Signature 4.- 10 Modular Equations in the Theory of Signature 4.- 11 The Theory for Signature 6.- 12 An Identity from the First Notebook and Further Hypergeometric Transformations.- 13 Some Enigmatic Formulas Near the End of the Third Notebook.- 14 Concluding Remarks.- 34 Class Invariants and Singular Moduli.- 1 Introduction.- 2 Table of Class Invariants.- 3 Computation of Gnand gnwhen 9/n.- 4 Kronecker’s Limit Formula and General Formulas for Class Invariants.- 5 Class Invariants Via Kronecker’s Limit Formula.- 6 Class Invariants Via Modular Equations.- 7 Class Invariants Via Class Field Theory.- 8 Miscellaneous Results.- 9 Singular Moduli.- 10 A Certain Rational Function of Singular Moduli.- 11 The Modular j-invariant.- 35 Values of Theta-Functions.- 0 Introduction.- 1 Elementary Values.- 2 Nonelementary Values of.- 3 A Remarkable Product of Theta-Functions.- 36 Modular Equations and Theta-Function Identities in Notebook 1.- 1 Modular Equations of Degree 3 and Related Theta-Function Identities.- 2 Modular Equations of Degree 5 and Related Theta-Function Identities.- 3 Other Modular Equations and Related Theta-Function Identities.- 4 Identities Involving Lambert Series.- 5 Identities Involving Eisenstein Series.- 6 Modular Equations in the Form of Schläfli.- 7 Modular Equations in the Form of Russell.- 8 Modular Equations in the Form of Weber.- 9 Series Transformations Associated with Theta-Functions.- 10 Miscellaneous Results.- 37 Infinite Series.- 38 Approximations and Asymptotic Expansions.- 39 Miscellaneous Results in the First Notebook.- Location of Entries in the Unorganized Portions of Ramanujan’s First Notebook.- References.