Ramanujan's lost notebook : Part I

By: Andrews, George EContributor(s): Berndt, Bruce CMaterial type: TextTextPublication details: USA: Springer, [c2005]Description: 437 pISBN: 9781493976256LOC classification: QA29.R3
Contents:
Introduction 1. Rogers-Ramanujan Continued Fraction and Its Modular Properties 2. Explicit Evaluations of the Rogers-Ramanujan Continued Fraction 3. A Fragment on the Rogers-Ramanujan and Cubic Continued Fractions 4. The Rogers-Ramanujan Continued Fraction and Its Connections with Partitions and Lambert Series 5. Finite Rogers-Ramanujan Continued Fractions 6. Other q-continued Fractions 7. Asymptotic Formulas for Continued Fractions 8. Ramanujan’s Continued Fraction for (q2;q3)∞/(q;q3)∞ 9. The Rogers-Fine Identity 10. An Empirical Study of the Rogers-Ramanujan Identities 11. Rogers-Ramanujan-Slater Type Identities 12. Partial Fractions 13. Hadamard Products for Two q-Series 14. Integrals of Theta Functions 15. Incomplete Elliptic Integrals 16. Infinite Integrals of q-Products 17. Modular Equations in Ramanujan’s Lost Notebook 18. Fragments on Lambert Series
Summary: 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 ofthe 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.
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Item type Current library Collection Shelving location Call number Status Notes Date due Barcode Item holds
Book Book ICTS
Mathematic Rack No 3 QA29.R3 (Browse shelf (Opens below)) Available Invoice no. IN00 6035; Date 07-01-2019 01487
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Introduction
1. Rogers-Ramanujan Continued Fraction and Its Modular Properties
2. Explicit Evaluations of the Rogers-Ramanujan Continued Fraction
3. A Fragment on the Rogers-Ramanujan and Cubic Continued Fractions
4. The Rogers-Ramanujan Continued Fraction and Its Connections with Partitions and Lambert Series
5. Finite Rogers-Ramanujan Continued Fractions
6. Other q-continued Fractions
7. Asymptotic Formulas for Continued Fractions
8. Ramanujan’s Continued Fraction for (q2;q3)∞/(q;q3)∞
9. The Rogers-Fine Identity
10. An Empirical Study of the Rogers-Ramanujan Identities
11. Rogers-Ramanujan-Slater Type Identities
12. Partial Fractions
13. Hadamard Products for Two q-Series
14. Integrals of Theta Functions
15. Incomplete Elliptic Integrals
16. Infinite Integrals of q-Products
17. Modular Equations in Ramanujan’s Lost Notebook
18. Fragments on Lambert Series

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 ofthe 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.

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