Ramanujan’s Lost Notebook Part I /

• Main Authors: Andrews, George E. (Author), Berndt, Bruce (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: New York, NY : Springer New York, 2005.
• Subjects: Mathematics.; Algebraic geometry.; Sequences (Mathematics).; Special functions.; Algebraic Geometry.; Sequences, Series, Summability.; Special Functions.

This volume is the first of approximately four volumes devoted to providing statements, proofs, and discussions of all the claims made by Srinivasa Ramanujan in his lost notebook and all his other manuscripts and letters published with the lost notebook. In addition to the lost notebook, this public...

Table of Contents:

• Inroduction
• 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)?/(q;q3)?
• 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.