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Author: Mohamed Nishad Maniparambath
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659513480
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This book is an introductory text on Theta function. It describes Classical Theta function, Ramanujan's Theta function and Cubic Theta function and Their developments and interconnection. This is designed for graduates and researchers as a start up material. The topics dealt with it includes Theta function as a solution of Heat conduction equation, elementary properties of Ramanujan's Theta function, One variable, Two variable, Three variable cubic theta functions and identities involving them.
Author: Mohamed Nishad Maniparambath
Publisher: LAP Lambert Academic Publishing
ISBN: 9783659513480
Category : Mathematics
Languages : en
Pages : 0
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Book Description
This book is an introductory text on Theta function. It describes Classical Theta function, Ramanujan's Theta function and Cubic Theta function and Their developments and interconnection. This is designed for graduates and researchers as a start up material. The topics dealt with it includes Theta function as a solution of Heat conduction equation, elementary properties of Ramanujan's Theta function, One variable, Two variable, Three variable cubic theta functions and identities involving them.
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: 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: Ratan Prakash Agarwal
Publisher: New Age International Limited Publishers
ISBN:
Category : Mathematics
Languages : en
Pages : 242
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Book Description
This Volume Is In Continuation Of Vol. I And Contains A Critical And Detailed Appraisal Of Ramanujans Work On Theta Functions And Partial Theta Functions, Mock Theta Functions Of Orders Three, Five, Seven And Six (Formally, Designated As Such By Andrews And Hickerson), Lambert Series And Their Relationship With Elliptic Functions, Mock Theta Functions And Allied Functions.A Characteristic Feature Of The Book Is A Detailed Discussion Of The Still Unsettled Problem Of Defining The Order Of A Mock Theta Function And A Discussion Of The Recently Defined Partial Mock Theta Functions And Their Import On Giving New Information On The Structure And Interrelationships Between Mock Theta Functions Of Certain Classes.
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: American Mathematical Soc.
ISBN: 0821841785
Category : Mathematics
Languages : en
Pages : 210
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Book Description
Ramanujan is recognized as one of the great number theorists of the twentieth century. Here now is the first book to provide an introduction to his work in number theory. Most of Ramanujan's work in number theory arose out of $q$-series and theta functions. This book provides an introduction to these two important subjects and to some of the topics in number theory that are inextricably intertwined with them, including the theory of partitions, sums of squares and triangular numbers, and the Ramanujan tau function. The majority of the results discussed here are originally due to Ramanujan or were rediscovered by him. Ramanujan did not leave us proofs of the thousands of theorems he recorded in his notebooks, and so it cannot be claimed that many of the proofs given in this book are those found by Ramanujan. However, they are all in the spirit of his mathematics. The subjects examined in this book have a rich history dating back to Euler and Jacobi, and they continue to be focal points of contemporary mathematical research. Therefore, at the end of each of the seven chapters, Berndt discusses the results established in the chapter and places them in both historical and contemporary contexts. The book is suitable for advanced undergraduates and beginning graduate students interested in number theory.
Author: Seung Hwan Son
Publisher:
ISBN:
Category :
Languages : en
Pages : 224
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Book Description
Author: Richard Bellman
Publisher: Courier Corporation
ISBN: 0486492958
Category : Mathematics
Languages : en
Pages : 100
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Book Description
Originally published: New York: Rinehart and Winston, 1961.
Author: Heng Huat Chan
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110540754
Category : Mathematics
Languages : en
Pages : 125
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Book Description
This book presents several results on elliptic functions and Pi, using Jacobi's triple product identity as a tool to show suprising connections between different topics within number theory such as theta functions, Eisenstein series, the Dedekind delta function, and Ramanujan's work on Pi. The included exercises make it ideal for both classroom use and self-study.
Author: Srinivasa Ramanujan Aiyangar
Publisher:
ISBN:
Category : Geometry
Languages : en
Pages : 382
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Book Description
