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Ramanujan’s Lost Notebook
ISBN-13:
9780387777665
Veröffentl:
2009
Seiten:
420
Autor:
George E. Andrews
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
1 - PDF Watermark
Sprache:
Englisch
Beschreibung:
This volume is the second of approximately four volumes that the authors plan to write on Ramanujan's lost notebook, which is broadly interpreted to include all material published in The Lost Notebook and Other Unpublished Papers in 1988.
"In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated "Ramanujan's lost notebook." 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."
The Heine Transformation.- The Sears#x2013; Thomae Transformation.- Bilateral Series.- Well-Poised Series.- Bailey#x02019;s Lemma and Theta Expansions.- Partial Theta Functions.- Special Identities.- Theta Function Identities.- Ramanujan#x02019;s Cubic Analogue of the Classical Ramanujan#x2013;Weber Class Invariants.- Miscellaneous Results on Elliptic Functions and Theta Functions.- Formulas for the Power Series Coefficients of Certain Quotients of Eisenstein Series.- Two Letters on Eisenstein Series Written from Matlock House.- Eisenstein Series and Modular Equations.- Series Representable in Terms of Eisenstein Series.- Eisenstein Series and Approximations to #x03C0;.- Miscellaneous Results on Eisenstein Series.
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