Chapter 16 of Ramanujan's Second Notebook: Theta-Functions and $q$-Series PDF Download
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Author: Chandrashekar Adiga
Publisher: American Mathematical Soc.
ISBN: 0821823167
Category : Mathematics
Languages : en
Pages : 99
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Book Description
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.
Author: Chandrashekar Adiga
Publisher: American Mathematical Soc.
ISBN: 0821823167
Category : Mathematics
Languages : en
Pages : 99
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Book Description
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.
Author: Shaun Cooper
Publisher: Springer
ISBN: 3319561723
Category : Mathematics
Languages : en
Pages : 696
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Book Description
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.
Author: Maruti Ram Murty
Publisher: American Mathematical Soc.
ISBN: 9780821870112
Category : Mathematics
Languages : en
Pages : 188
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Book Description
This book contains lectures on theta functions written by experts well known for excellence in exposition. The lectures represent the content of four courses given at the Centre de Recherches Mathematiques in Montreal during the academic year 1991-1992, which was devoted to the study of automorphic forms. Aimed at graduate students, the book synthesizes the classical and modern points of view in theta functions, concentrating on connections to number theory and representation theory. An excellent introduction to this important subject of current research, this book is suitable as a text in advanced graduate courses.
Author: George E. Andrews
Publisher: Springer Science & Business Media
ISBN: 0387777660
Category : Mathematics
Languages : en
Pages : 423
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Book Description
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.
Author: Bruce C. Berndt
Publisher: Springer Science & Business Media
ISBN: 146120965X
Category : Mathematics
Languages : en
Pages : 521
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Book Description
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.
Author: Mourad E. H. Ismail
Publisher: Springer Science & Business Media
ISBN: 0387242333
Category : Mathematics
Languages : en
Pages : 497
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Book Description
A collection of articles on various aspects of q-series and special functions dedicated to Mizan Rahman. It also includes an article by Askey, Ismail, and Koelink on Rahman’s mathematical contributions and how they influenced the recent upsurge in the subject.
Author: Leon Ehrenpreis
Publisher: American Mathematical Soc.
ISBN: 0821814842
Category : Mathematics
Languages : en
Pages : 378
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Book Description
Author: George E. Andrews
Publisher: American Mathematical Soc.
ISBN: 9780821889114
Category : Mathematics
Languages : en
Pages : 146
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Book Description
Author: Joaquin Bustoz
Publisher: Springer Science & Business Media
ISBN: 9401008183
Category : Mathematics
Languages : en
Pages : 521
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Book Description
The Advanced Study Institute brought together researchers in the main areas of special functions and applications to present recent developments in the theory, review the accomplishments of past decades, and chart directions for future research. Some of the topics covered are orthogonal polynomials and special functions in one and several variables, asymptotic, continued fractions, applications to number theory, combinatorics and mathematical physics, integrable systems, harmonic analysis and quantum groups, Painlevé classification.
Author: Krishnaswami Alladi
Publisher: Lecture Notes in Mathematics
ISBN:
Category : Mathematics
Languages : en
Pages : 254
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Book Description
