Ramanujan's Lost Notebook

Part I
Softcover Nachdruck of hardcover 1. Auflage 2005
ISBN: 978-1-4419-2062-1
Verlag: Springer

Buch, Englisch, 438 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 680 g

In the library at Trinity College, Cambridge in 1976, George Andrews of Pennsylvania State University discovered a sheaf of pages in the handwriting of Srinivasa Ramanujan. Soon designated as "Ramanujan’s Lost Notebook," it contains considerable material on mock theta functions and undoubtedly dates from the last year of Ramanujan’s life. In this book, the notebook is presented with additional material and expert commentary.

Zielgruppe

Research

Autoren/Hrsg.

Berndt, Bruce C.

Andrews, George E.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

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.

Über Autor(innen)

George E. Andrews is currently a professor of mathematics at Pennsylvania State University.

Bruce C. Berndt is currently a professor of mathematics at the University of Illinois.