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"Ramanujan’s Notebooks"

♥ Book Title : Ramanujan’s Notebooks
♣ Name Author : Bruce C. Berndt
∞ Launching : 2012-12-06
◊ Info ISBN Link : 9781461216247
⊗ Detail ISBN code : 1461216249
⊕ Number Pages : Total 624 sheet
♮ News id : O8XcBwAAQBAJ

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☯ Full Synopsis : "The fifth and final volume to establish the results claimed by the great Indian mathematician Srinivasa Ramanujan in his "Notebooks" first published in 1957. Although each of the five volumes contains many deep results, the average depth in this volume is possibly greater than in the first four. There are several results on continued fractions - a subject that Ramanujan loved very much. It is the authors wish that this and previous volumes will serve as springboards for further investigations by mathematicians intrigued by Ramanujans remarkable ideas."Article| Bruce C. Berndt| Statement ..."

"Ramanujan's Lost Notebook"

♥ Book Title : Ramanujan's Lost Notebook
♣ Name Author : George E. Andrews
∞ Launching : 2013-06-04
◊ Info ISBN Link : 9781461440819
⊗ Detail ISBN code : 1461440815
⊕ Number Pages : Total 439 sheet
♮ News id : 6Z5GAAAAQBAJ

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☯ Full Synopsis : "​​​​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 volume is the fourth of five volumes that the authors plan to write on Ramanujan’s lost notebook.​ In contrast to the first three books on Ramanujan's Lost Notebook, the fourth book does not focus on q-series. Most of the entries examined in this volume fall under the purviews of number theory and classical analysis. Several incomplete manuscripts of Ramanujan published by Narosa with the lost notebook are discussed. Three of the partial manuscripts are on diophantine approximation, and others are in classical Fourier analysis and prime number theory. Most of the entries in number theory fall under the umbrella of classical analytic number theory. Perhaps the most intriguing entries are connected with the classical, unsolved circle and divisor problems. 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​"Article| George E. Andrews| Statement ..."

"The Lost Notebook and Other Unpublished Papers"

♥ Book Title : The Lost Notebook and Other Unpublished Papers
♣ Name Author : S. Ramanujan
∞ Launching : 2008-01-01
◊ Info ISBN Link : 1842655078
⊗ Detail ISBN code : 9781842655078
⊕ Number Pages : Total 419 sheet
♮ News id : CSXcOgAACAAJ

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☯ Full Synopsis : "Covers q-series and related topics including mock functions, 60 per cent Modular equations and relations, singular moduli, 30 per cent Integrals, Dirichlet series, congruences, asymptotics, miscellaneous."Article| S. Ramanujan| Statement ..."

"Ramanujan’s Lost Notebook"

♥ Book Title : Ramanujan’s Lost Notebook
♣ Name Author : George E. Andrews
∞ Launching :
◊ Info ISBN Link : 9783319778341
⊗ Detail ISBN code : 331977834X
⊕ Number Pages : Total 233 sheet
♮ News id : cDBtDwAAQBAJ

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☯ Full Synopsis : ""Article| George E. Andrews| Statement ..."

"Ramanujan's Lost Notebook"

♥ Book Title : Ramanujan's Lost Notebook
♣ Name Author : George E Andrews
∞ Launching : 2013-06-30
◊ Info ISBN Link : 1461440823
⊗ Detail ISBN code : 9781461440826
⊕ Number Pages : Total 460 sheet
♮ News id : N_UivwEACAAJ

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☯ Full Synopsis : ""Article| George E Andrews| Statement ..."

"Collected Papers of Srinivasa Ramanujan"

♥ Book Title : Collected Papers of Srinivasa Ramanujan
♣ Name Author : Srinivasa Ramanujan Aiyangar
∞ Launching : 1927
◊ Info ISBN Link : 9780821820766
⊗ Detail ISBN code : 0821820761
⊕ Number Pages : Total 426 sheet
♮ News id : oSioAM4wORMC

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☯ Full Synopsis : "The influence of Ramanujan on number theory is without parallel in mathematics. His papers, problems, and letters have spawned a remarkable number of later results by many different mathematicians. Here, his 37 published papers, most of his first two and last letters to Hardy, the famous 58 problems submitted to the Journal of the Indian Mathematical Society, and the commentary of the original editors (Hardy, Seshu Aiyar and Wilson) are reprinted again, after having been unavailable for some time. In this printing of Ramanujan's collected papers, Bruce Berndt provides an annotated guide to Ramanujan's work and to the mathematics it inspired over the last three-quarters of a century. The historical development of ideas is traced in the commentary and by citations to the copious references. The editor has done the mathematical world a tremendous service that few others would be qualified to do."Article| Srinivasa Ramanujan Aiyangar| Statement ..."

"Ramanujan’s Notebooks"

♥ Book Title : Ramanujan’s Notebooks
♣ Name Author : Bruce C. Berndt
∞ Launching : 2012-12-06
◊ Info ISBN Link : 9781461208792
⊗ Detail ISBN code : 1461208793
⊕ Number Pages : Total 451 sheet
♮ News id : QoMHCAAAQBAJ

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☯ Full Synopsis : "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."Article| Bruce C. Berndt| Statement ..."

"Number Theory in the Spirit of Ramanujan"

♥ Book Title : Number Theory in the Spirit of Ramanujan
♣ Name Author : Bruce C. Berndt
∞ Launching : 2006
◊ Info ISBN Link : 9780821841785
⊗ Detail ISBN code : 0821841785
⊕ Number Pages : Total 187 sheet
♮ News id : bbLxBwAAQBAJ

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☯ Full Synopsis : "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."Article| Bruce C. Berndt| Statement ..."

"The Lost Notebook and Other Unpublished Papers"

♥ Book Title : The Lost Notebook and Other Unpublished Papers
♣ Name Author : Srinivasa Ramanujan Aiyangar
∞ Launching : 1988
◊ Info ISBN Link : 038718726X
⊗ Detail ISBN code : 9780387187266
⊕ Number Pages : Total 419 sheet
♮ News id : 0PRfQgAACAAJ

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☯ Full Synopsis : "The so-called Lost Notebook of S.R. Ramanujan was brought to light in 1976 as part of the Watson bequest, by G.E. Andrews with whose introduction this collection of unpublished manuscripts opens. A major portion of the Lost Notebook - really just 90 unpaginated sheets of work on q-series and other topics - is reproduced here in facsimile. Letters from Ramanujan to Hardy as well as various other sheets of seemingly related notes are then included, on topics including coefficients in the 1/q3 and 1/q2 problems and the mock theta functions. The next 180 pages consist of unpublished manuscripts of Ramanujan, including 28 pages from the 'Loose Papers` held in the Trinity College Library. Finally a number of interesting letters that were exchanged between Ramanujan, Littlewood, Hardy and Watson, with a bearing on Ramanujan's work are collected together here with other extracts and fragments."Article| Srinivasa Ramanujan Aiyangar| Statement ..."

"Ramanujan’s Notebooks"

♥ Book Title : Ramanujan’s Notebooks
♣ Name Author : Bruce C. Berndt
∞ Launching : 1997-12-12
◊ Info ISBN Link : 0387949410
⊗ Detail ISBN code : 9780387949413
⊕ Number Pages : Total 624 sheet
♮ News id : Z__xZ9pNkZMC

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☯ Full Synopsis : "The fifth and final volume to establish the results claimed by the great Indian mathematician Srinivasa Ramanujan in his "Notebooks" first published in 1957. Although each of the five volumes contains many deep results, the average depth in this volume is possibly greater than in the first four. There are several results on continued fractions - a subject that Ramanujan loved very much. It is the authors wish that this and previous volumes will serve as springboards for further investigations by mathematicians intrigued by Ramanujans remarkable ideas."Article| Bruce C. Berndt| Statement ..."

"Q-series"

♥ Book Title : Q-series
♣ Name Author : George E. Andrews
∞ Launching : 1986-01-01
◊ Info ISBN Link : 0821889117
⊗ Detail ISBN code : 9780821889114
⊕ Number Pages : Total 130 sheet
♮ News id : 6aPO5PUh4qAC

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☯ Full Synopsis : ""Article| George E. Andrews| Statement ..."

"Handbook of Continued Fractions for Special Functions"

♥ Book Title : Handbook of Continued Fractions for Special Functions
♣ Name Author : Annie A.M. Cuyt
∞ Launching : 2008-04-12
◊ Info ISBN Link : 1402069499
⊗ Detail ISBN code : 9781402069499
⊕ Number Pages : Total 431 sheet
♮ News id : DQtpJaEs4NIC

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☯ Full Synopsis : "Special functions are pervasive in all fields of science and industry. The most well-known application areas are in physics, engineering, chemistry, computer science and statistics. Because of their importance, several books and websites (see for instance http: functions.wolfram.com) and a large collection of papers have been devoted to these functions. Of the standard work on the subject, the Handbook of mathematical functions with formulas, graphs and mathematical tables edited by Milton Abramowitz and Irene Stegun, the American National Institute of Standards claims to have sold over 700 000 copies! But so far no project has been devoted to the systematic study of continued fraction representations for these functions. This handbook is the result of such an endeavour. We emphasise that only 10% of the continued fractions contained in this book, can also be found in the Abramowitz and Stegun project or at the Wolfram website!"Article| Annie A.M. Cuyt| Statement ..."