Chapter 16 Of Ramanujan S Second Notebook Theta Functions And Q Series
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Chapter 16 Of Ramanujan S Second Notebook
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Author : Chandrashekar Adiga
language : en
Publisher:
Release Date : 1985
Chapter 16 Of Ramanujan S Second Notebook written by Chandrashekar Adiga and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Electronic books categories.
Chapter 16 Of Ramanujan S Second Notebook
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Author : Srinivasa Ramanujan Aiyangar
language : en
Publisher:
Release Date : 1985
Chapter 16 Of Ramanujan S Second Notebook written by Srinivasa Ramanujan Aiyangar and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Functions, Theta categories.
The first part of Chapter 16 in Ramanujan's second notebook is devoted to q-series. Several of the results obtained by Ramanujan are classical, but many are new. In particular, certain elegant q-continued fraction expansions have not appeared heretofore in print. In the remainder of this chapter, Ramanujan develops the theory of the classical theta-functions in a manner different from his nineteenth century predecessors such as Jacobi. Although many of Ramanujan's discoveries about theta-functions are well-known, several new results are also to be found.
Chapter 16 Of Ramanujan S Second Notebook Theta Functions And Q Series
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Author : Chandrashekar Adiga
language : en
Publisher: American Mathematical Soc.
Release Date : 1985
Chapter 16 Of Ramanujan S Second Notebook Theta Functions And Q Series written by Chandrashekar Adiga and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
The first part of Chapter 16 in Ramanujan's second notebook is devoted to q-series. Several of the results obtained by Ramanujan are classical, but many are new. In particular, certain elegant q-continued fraction expansions have not appeared heretofore in print. In the remainder of this chapter, Ramanujan develops the theory of the classical theta-functions in a manner different from his nineteenth century predecessors such as Jacobi. Although many of Ramanujan's discoveries about theta-functions are well-known, several new results are also to be found.
Chapter 16 Of Ramanujan S Second Notebook
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Author : Albert Baernstein
language : en
Publisher:
Release Date : 1985
Chapter 16 Of Ramanujan S Second Notebook written by Albert Baernstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Banach spaces categories.
Ramanujan S Notebooks
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Author : Bruce C. Berndt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Ramanujan S Notebooks written by Bruce C. Berndt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Ramanujan S Theta Functions
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Author : Shaun Cooper
language : en
Publisher: Springer
Release Date : 2017-06-12
Ramanujan S Theta Functions written by Shaun Cooper and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-06-12 with Mathematics categories.
Theta functions were studied extensively by Ramanujan. This book provides a systematic development of Ramanujan’s results and extends them to a general theory. The author’s treatment of the subject is comprehensive, providing a detailed study of theta functions and modular forms for levels up to 12. Aimed at advanced undergraduates, graduate students, and researchers, the organization, user-friendly presentation, and rich source of examples, lends this book to serve as a useful reference, a pedagogical tool, and a stimulus for further research. Topics, especially those discussed in the second half of the book, have been the subject of much recent research; many of which are appearing in book form for the first time. Further results are summarized in the numerous exercises at the end of each chapter.
Ramanujan S Notebooks
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Author : Bruce C. Berndt
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Ramanujan S Notebooks written by Bruce C. Berndt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
During the years 1903-1914, Ramanujan worked in almost complete isolation in India. During this time, he recorded most of his mathematical discoveries without proofs in notebooks. Although many of his results were already found in the literature, most were not. Almost a decade after Ramanujan's death in 1920, G.N. Watson and B.M. Wilson began to edit Ramanujan's notebooks, but they never completed the task. A photostat edition, with no editing, was published by the Tata Institute of Fundamental Research in Bombay in 1957. This book is the fourth of five volumes devoted to the editing of Ramanujan's notebooks. Parts I, II, and III, published in 1985, 1989, and 1991, contain accounts of Chapters 1-21 in Ramanujan's second notebook as well as a description of his quarterly reports. This is the first of two volumes devoted to proving the results found in the unorganized portions of the second notebook and in the third notebook. The author also proves those results in the first notebook that are not found in the second or third notebooks. For those results that are known, references in the literature are provided. Otherwise, complete proofs are given. Over 1/2 of the results in the notebooks are new. Many of them are so startling and different that there are no results akin to them in the literature.
Number Theory
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Author : Krishnaswami Alladi
language : en
Publisher: Springer
Release Date : 2006-11-14
Number Theory written by Krishnaswami Alladi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
Ramanujan 125
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Author : Ae Ja Yee,
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-10-14
Ramanujan 125 written by Ae Ja Yee, and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-10-14 with Mathematics categories.
This volume contains the proceedings of an international conference to commemorate the 125th anniversary of Ramanujan's birth, held from November 5-7, 2012, at the University of Florida, Gainesville, Florida. Srinivasa Ramanujan was India's most famous mathematician. This volume contains research and survey papers describing recent and current developments in the areas of mathematics influenced by Ramanujan. The topics covered include modular forms, mock theta functions and harmonic Maass forms, continued fractions, partition inequalities, -series, representations of affine Lie algebras and partition identities, highly composite numbers, analytic number theory and quadratic forms.
Theta Functions Bowdoin 1987 Part 2
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Author : Leon Ehrenpreis
language : en
Publisher: American Mathematical Soc.
Release Date : 1989
Theta Functions Bowdoin 1987 Part 2 written by Leon Ehrenpreis and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.