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Author : Chandrashekar Adiga
Publisher :
ISBN 13 : 9781470407285
Total Pages : 0 pages
Book Rating : 4.4/5 (72 download)
Download or read book Chapter 16 of Ramanujan's Second Notebook written by Chandrashekar Adiga and published by . This book was released on 1985 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Chandrashekar Adiga
Publisher : American Mathematical Soc.
ISBN 13 : 0821823167
Total Pages : 99 pages
Book Rating : 4.8/5 (218 download)
Download or read book Chapter 16 of Ramanujan's Second Notebook: Theta-Functions and $q$-Series written by Chandrashekar Adiga and published by American Mathematical Soc.. This book was released on 1985 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 :
Publisher :
ISBN 13 :
Total Pages : 85 pages
Book Rating : 4.:/5 (859 download)
Download or read book Chapter 16 of Ramanujan's Second Notebook: Theta-functions and Q-series written by and published by . This book was released on 1985 with total page 85 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Albert Baernstein
Publisher :
ISBN 13 : 9780821823156
Total Pages : 82 pages
Book Rating : 4.8/5 (231 download)
Download or read book Chapter 16 of Ramanujan's Second Notebook written by Albert Baernstein and published by . This book was released on 1985 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Bruce C. Berndt
Publisher : Springer Science & Business Media
ISBN 13 : 146120965X
Total Pages : 521 pages
Book Rating : 4.4/5 (612 download)
Download or read book Ramanujan’s Notebooks written by Bruce C. Berndt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : George E Andrews
Publisher : World Scientific
ISBN 13 : 9811277389
Total Pages : 704 pages
Book Rating : 4.8/5 (112 download)
Download or read book Analytic And Combinatorial Number Theory: The Legacy Of Ramanujan - Contributions In Honor Of Bruce C. Berndt written by George E Andrews and published by World Scientific. This book was released on 2024-08-19 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects the contributions stemming from the conference Analytic and Combinatorial Number Theory: The Legacy of Ramanujan which took place at the University of Illinois at Urbana-Champaign on June 6-9, 2019. The conference included 26 plenary talks, 71 contributed talks, and 170 participants. As was the case for the conference, this book is in honor of Bruce C Berndt and in celebration of his mathematics and his 80th birthday.Along with a number of papers previously appearing in Special Issues of the International Journal of Number Theory, the book collects together a few more papers, a biography of Bruce by Atul Dixit and Ae Ja Yee, a preface by George Andrews, a gallery of photos from the conference, a number of speeches from the conference banquet, the conference poster, a list of Bruce's publications at the time this volume was created, and a list of the talks from the conference.
Author : Shaun Cooper
Publisher : Springer
ISBN 13 : 3319561723
Total Pages : 696 pages
Book Rating : 4.3/5 (195 download)
Download or read book Ramanujan's Theta Functions written by Shaun Cooper and published by Springer. This book was released on 2017-06-12 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Krishnaswami Alladi
Publisher : Springer
ISBN 13 : 354039642X
Total Pages : 224 pages
Book Rating : 4.5/5 (43 download)
Download or read book Number Theory written by Krishnaswami Alladi and published by Springer. This book was released on 2006-11-14 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Leon Ehrenpreis
Publisher : American Mathematical Soc.
ISBN 13 : 0821814842
Total Pages : 378 pages
Book Rating : 4.8/5 (218 download)
Download or read book Theta Functions-Bowdoin 1987, Part 2 written by Leon Ehrenpreis and published by American Mathematical Soc.. This book was released on 1989 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Ae Ja Yee,
Publisher : American Mathematical Soc.
ISBN 13 : 1470410788
Total Pages : 186 pages
Book Rating : 4.4/5 (74 download)
Download or read book Ramanujan 125 written by Ae Ja Yee, and published by American Mathematical Soc.. This book was released on 2014-10-14 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Author : Bruce C. Berndt
Publisher : American Mathematical Soc.
ISBN 13 : 9780821826249
Total Pages : 388 pages
Book Rating : 4.8/5 (262 download)
Download or read book Ramanujan: Essays and Surveys written by Bruce C. Berndt and published by American Mathematical Soc.. This book was released on 2001 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains essays on Ramanujan and his work that were written especially for this volume. It also includes important survey articles in areas influenced by Ramanujan's mathematics. Most of the articles in the book are nontechnical, but even those that are more technical contain substantial sections that will engage the general reader. The book opens with the only four existing photographs of Ramanujan, presenting historical accounts of them and information about other people in the photos. This section includes an account of a cryptic family history written by his younger brother, S. Lakshmi Narasimhan. Following are articles on Ramanujan's illness by R. A. Rankin, the British physician D. A. B. Young, and Nobel laureate S. Chandrasekhar. They present a study of his symptoms, a convincing diagnosis of the cause of his death, and a thorough exposition of Ramanujan's life as a patient in English sanitariums and nursing homes. Following this are biographies of S. Janaki (Mrs. Ramanujan) and S. Narayana Iyer, Chief Accountant of the Madras Port Trust Office, who first communicated Ramanujan's work to the Journal of the Indian Mathematical Society. The last half of the book begins with a section on ``Ramanujan's Manuscripts and Notebooks''. Included is an important article by G. E. Andrews on Ramanujan's lost notebook. The final two sections feature both nontechnical articles, such as Jonathan and Peter Borwein's ``Ramanujan and pi'', and more technical articles by Freeman Dyson, Atle Selberg, Richard Askey, and G. N. Watson. This volume complements the book Ramanujan: Letters and Commentary, Volume 9, in the AMS series, History of Mathematics. For more on Ramanujan, see these AMS publications Ramanujan: Twelve Lectures on Subjects Suggested by His Life and Work, Volume 136.H, and Collected Papers of Srinivasa Ramanujan, Volume 159.H, in the AMS Chelsea Publishing series.
Author : A.M. Mathai
Publisher : Springer Science & Business Media
ISBN 13 : 0387758941
Total Pages : 480 pages
Book Rating : 4.3/5 (877 download)
Download or read book Special Functions for Applied Scientists written by A.M. Mathai and published by Springer Science & Business Media. This book was released on 2008-02-13 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written by a highly distinguished author, provides the required mathematical tools for researchers active in the physical sciences. The book presents a full suit of elementary functions for scholars at PhD level. The opening chapter introduces elementary classical special functions. The final chapter is devoted to the discussion of functions of matrix argument in the real case. The text and exercises have been class-tested over five different years.
Author : George E. Andrews
Publisher : American Mathematical Soc.
ISBN 13 : 9780821889114
Total Pages : 146 pages
Book Rating : 4.8/5 (891 download)
Download or read book Q-series written by George E. Andrews and published by American Mathematical Soc.. This book was released on 1986-01-01 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Shaun Cooper
Publisher : World Scientific
ISBN 13 : 9814366463
Total Pages : 185 pages
Book Rating : 4.8/5 (143 download)
Download or read book Development of Elliptic Functions According to Ramanujan written by Shaun Cooper and published by World Scientific. This book was released on 2012 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique book provides an innovative and efficient approach to elliptic functions, based on the ideas of the great Indian mathematician Srinivasa Ramanujan. The original 1988 monograph of K Venkatachaliengar has been completely revised. Many details, omitted from the original version, have been included, and the book has been made comprehensive by notes at the end of each chapter. The book is for graduate students and researchers in Number Theory and Classical Analysis, as well for scholars and aficionados of Ramanujan''s work. It can be read by anyone with some undergraduate knowledge of real and complex analysis.
Author : George E. Andrews
Publisher : American Mathematical Soc.
ISBN 13 : 0821825380
Total Pages : 82 pages
Book Rating : 4.8/5 (218 download)
Download or read book The Continued Fractions Found in the Unorganized Portions of Ramanujan's Notebooks written by George E. Andrews and published by American Mathematical Soc.. This book was released on 1992 with total page 82 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among his thirty-three published papers, Ramanujan had only one continued fraction, the Rogers-Ramanujan continued fraction. However, his notebooks contain over 100 results on continued fractions. At the end of his second notebook are 100 pages of unorganized material, and the third notebook comprises thirty-three pages of disorganized results. In these 133 pages of material are approximately sixty theorems on continued fractions, most of them new results. In this monograph, the authors discuss and prove each of these theorems. Aimed at those interested in Ramanujan and his work, this monograph will be of special interest to those who work in continued fractions q -series, special function, theta-functions, and combinatorics. The work is likely to be of interest to those in number theory as well. The only required background is some knowledge of continued fractions and a course in complex analysis.
Author : Krishnaswami Alladi
Publisher : Springer Nature
ISBN 13 : 9811562415
Total Pages : 265 pages
Book Rating : 4.8/5 (115 download)
Download or read book Ramanujan's Place in the World of Mathematics written by Krishnaswami Alladi and published by Springer Nature. This book was released on 2021-09-17 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: The First Edition of the book is a collection of articles, all by the author, on the Indian mathematical genius Srinivasa Ramanujan as well as on some of the greatest mathematicians in history whose life and works have things in common with Ramanujan. It presents a unique comparative study of Ramanujan’s spectacular discoveries and remarkable life with the monumental contributions of various mathematical luminaries, some of whom, like Ramanujan, overcame great difficulties in life. Also, among the articles are reviews of three important books on Ramanujan’s mathematics and life. In addition, some aspects of Ramanujan’s contributions, such as his remarkable formulae for the number pi, his path-breaking work in the theory of partitions, and his fundamental observations on quadratic forms, are discussed. Finally, the book describes various current efforts to ensure that the legacy of Ramanujan will be preserved and continue to thrive in the future. This Second Edition is an expanded version of the first with six more articles by the author. Of note is the inclusion of a detailed review of the movie The Man Who Knew Infinity, a description of the fundamental work of the SASTRA Ramanujan Prize Winners, and an account of the Royal Society Conference to honour Ramanujan’s legacy on the centenary of his election as FRS.
Author : K. Srinivasa Rao
Publisher : Springer Nature
ISBN 13 : 9811604479
Total Pages : 299 pages
Book Rating : 4.8/5 (116 download)
Download or read book Srinivasa Ramanujan written by K. Srinivasa Rao and published by Springer Nature. This book was released on 2021-05-30 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a unique account on the life and works of Srinivasa Ramanujan—often hailed as the greatest “natural” mathematical genius. Sharing valuable insights into the many stages of Ramanujan’s life, this book provides glimpses into his prolific research on highly composite numbers, partitions, continued fractions, mock theta functions, arithmetic, and hypergeometric functions which led the author to discover a new summation theorem. It also includes the list of Ramanujan’s collected papers, letters and other material present at the Wren Library, Trinity College in Cambridge, UK. This book is a valuable resource for all readers interested in Ramanujan’s life, work and indelible contributions to mathematics.
