- Gebundenes Buch
- Merkliste
- Auf die Merkliste
- Bewerten Bewerten
- Teilen
- Produkt teilen
- Produkterinnerung
- Produkterinnerung
This book constitutes 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, perhaps the average depth in this volume is greater than in the first four. There are several results on continued fractions a subject that Ramanujan loved very much. It is the author's wish that this volume and previous volumes will serve as springboards for further investigations by mathematicians intrigued by Ramanujan's remarkable ideas.
Andere Kunden interessierten sich auch für
- George E. AndrewsRamanujan's Lost Notebook153,99 €
- Berndt ( Ed. )Surveys in Number Theory82,99 €
- Pierre Cartier / Bernard Julia / Pierre Moussa / Pierre Vanhove (eds.)Frontiers in Number Theory, Physics, and Geometry I115,99 €
- Paulo RibenboimMy Numbers, My Friends58,99 €
- Janos SuranyiTopics in the Theory of Numbers93,99 €
- Benjamin FineThe Fundamental Theorem of Algebra42,99 €
- Benjamin FineThe Fundamental Theorem of Algebra57,99 €
-
-
-
This book constitutes 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, perhaps the average depth in this volume is greater than in the first four. There are several results on continued fractions a subject that Ramanujan loved very much. It is the author's wish that this volume and previous volumes will serve as springboards for further investigations by mathematicians intrigued by Ramanujan's remarkable ideas.
Produktdetails
- Produktdetails
- Verlag: Springer / Springer New York / Springer, Berlin
- Artikelnr. des Verlages: 978-0-387-94941-3
- Repr. d. Ausg. v. 1997
- Seitenzahl: 644
- Erscheinungstermin: 12. Dezember 1997
- Englisch
- Abmessung: 241mm x 160mm x 40mm
- Gewicht: 1121g
- ISBN-13: 9780387949413
- ISBN-10: 0387949410
- Artikelnr.: 21471346
- Verlag: Springer / Springer New York / Springer, Berlin
- Artikelnr. des Verlages: 978-0-387-94941-3
- Repr. d. Ausg. v. 1997
- Seitenzahl: 644
- Erscheinungstermin: 12. Dezember 1997
- Englisch
- Abmessung: 241mm x 160mm x 40mm
- Gewicht: 1121g
- ISBN-13: 9780387949413
- ISBN-10: 0387949410
- Artikelnr.: 21471346
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.
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.