Theorems on Theta Functions in Ramanujan's Lost Notebook PDF Download
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Author: Seung Hwan Son
Publisher:
ISBN:
Category :
Languages : en
Pages : 224
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Book Description
Author: Seung Hwan Son
Publisher:
ISBN:
Category :
Languages : en
Pages : 224
Get Book Here
Book Description
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: George E. Andrews
Publisher: Springer Science & Business Media
ISBN: 9780387255293
Category : Biography & Autobiography
Languages : en
Pages : 460
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Book Description
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.
Author: George E. Andrews
Publisher: Springer
ISBN: 331977834X
Category : Mathematics
Languages : en
Pages : 430
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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." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This fifth and final installment of the authors’ examination of Ramanujan’s lost notebook focuses on the mock theta functions first introduced in Ramanujan’s famous Last Letter. This volume proves all of the assertions about mock theta functions in the lost notebook and in the Last Letter, particularly the celebrated mock theta conjectures. Other topics feature Ramanujan’s many elegant Euler products and the remaining entries on continued fractions not discussed in the preceding volumes. Review from the second volume:"Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited."- MathSciNet Review from the first volume:"Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete."- Gazette of the Australian Mathematical Society
Author: Nathan Jacob Fine
Publisher: American Mathematical Soc.
ISBN: 0821815245
Category : Mathematics
Languages : en
Pages : 142
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Book Description
The theory of partitions, founded by Euler, has led in a natural way to the idea of basic hypergeometric series, also known as Eulerian series. These series were first studied systematically by Heine, but many early results are attributed to Euler, Gauss, and Jacobi. This book provides a simple approach to basic hypergeometric series.
Author: George E. Andrews
Publisher: Springer
ISBN: 9783319778327
Category : Mathematics
Languages : en
Pages : 430
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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." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony. This fifth and final installment of the authors’ examination of Ramanujan’s lost notebook focuses on the mock theta functions first introduced in Ramanujan’s famous Last Letter. This volume proves all of the assertions about mock theta functions in the lost notebook and in the Last Letter, particularly the celebrated mock theta conjectures. Other topics feature Ramanujan’s many elegant Euler products and the remaining entries on continued fractions not discussed in the preceding volumes. Review from the second volume:"Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited."- MathSciNet Review from the first volume:"Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete."- Gazette of the Australian Mathematical Society
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: George E. Andrews
Publisher: Springer
ISBN: 9780387255293
Category : Mathematics
Languages : en
Pages : 438
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Book Description
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.
Author: Srinivasa Ramanujan Aiyangar
Publisher:
ISBN:
Category : Geometry
Languages : en
Pages : 382
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Book Description
Author: George E. Andrews
Publisher: Springer
ISBN: 9780387255293
Category : Mathematics
Languages : en
Pages : 438
Get Book Here
Book Description
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.
