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Ramanujan's Notebooks de Bruce C. Berndt

Ramanujan's Notebooks

Autor Bruce C. Berndt
en Limba Engleză Hardback – 23 iul 1991
Upon Ramanujans death in 1920, G. H. Hardy strongly urged that Ramanujans notebooks be published and edited. In 1957, the Tata Institute of Fundamental Research in Bombay finally published a photostat edition of the notebooks, but no editing was undertaken. In 1977, Berndt began the task of editing Ramanujans notebooks: proofs are provided to theorems not yet proven in previous literature, and many results are so startling as to be unique.
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Specificații

ISBN-13: 9780387975030
ISBN-10: 0387975039
Pagini: 528
Ilustrații: XIII, 510 p.
Dimensiuni: 160 x 241 x 34 mm
Greutate: 0.95 kg
Ediția:1st ed. 1991. Corr. 2nd printing 1997
Editura: Springer
Locul publicării:New York, NY, United States

Public țintă

Research

Descriere

During the time period between 1903 and 1914, Ramanujan worked in almost complete isolation in India. Throughout these years, he recorded his mathematical results without proofs in notebooks. Upon Ramanujan's death in 1920, G.H. Hardy strongly urged that Ramanujan's notebooks be published and edited. The English mathematicians G.N. Watson and B.M. Wilson began this task in 1929, but although they devoted nearly ten years to the project, the work was never completed. In 1957, the Tata Institute of Fundamental Research in Bombay published a photostat edition of the notebooks, but no editing was undertaken. In 1977, Berndt began the tasks of editing Ramanujan's notebooks. Proofs are provided to theorems not yet proven in previous literature, and many results are so startling and different that there are no results akin to them in the literature.

Cuprins

16 q-Series and Theta-Functions.- 17 Fundamental Properties of Elliptic Functions.- 18 The Jacobian Elliptic Functions.- 19 Modular Equations of Degrees 3, 5, and 7 and Associated Theta-Function Identities.- 20 Modular Equations of Higher and Composite Degrees.- 21 Eisenstein Series.- References.