Ramanujan's Lost Notebook
Part I
(Sprache: Englisch)
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...
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Klappentext zu „Ramanujan's Lost Notebook “
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.
Inhaltsverzeichnis zu „Ramanujan's Lost Notebook “
Preface.- Introduction.- The 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)8/(q; q3)8.- 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.- Location Guide.- Provenance.- References.- Index.
Autoren-Porträt von George E. Andrews, Bruce C. Berndt
In the spring of 1976, George Andrews of Pennsylvania State University found "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. 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.
Bibliographische Angaben
- Autoren: George E. Andrews , Bruce C. Berndt
- 2010, Softcover reprint of hardcover 1st ed. 2005, XIV, 438 Seiten, Masse: 15,5 x 23,5 cm, Kartoniert (TB), Englisch
- Verlag: Springer, Berlin
- ISBN-10: 1441920625
- ISBN-13: 9781441920621
Sprache:
Englisch
Pressezitat
hematicians interested in the work of Ramanujan, will delight in studying this book ... ." (Andrew V. Sills, Mathematical Reviews, Issue 2005 m)Kommentar zu "Ramanujan's Lost Notebook"
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