The Mathematical Legacy of Srinivasa Ramanujan, M. Ram Murty; V. Kumar Murty

Автор: Bernard Candelpergher
Название: Ramanujan Summation of Divergent Series
ISBN: 3319636294 ISBN-13(EAN): 9783319636290
Издательство: Springer
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Описание: The aim of this monograph is to give a detailed exposition of the summation method that Ramanujan uses in Chapter VI of his second Notebook. This provides simple proofs of theorems on the summation of some divergent series. Finally, in the last chapter, a purely algebraic theory is developed that unifies all these summation processes.

Автор: George E. Andrews; Bruce C. Berndt
Название: Ramanujan`s Lost Notebook
ISBN: 1441920625 ISBN-13(EAN): 9781441920621
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Описание: 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.

Автор: George E. Andrews; Bruce C. Berndt
Название: Ramanujan`s Lost Notebook
ISBN: 1489991751 ISBN-13(EAN): 9781489991751
Издательство: Springer
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Описание: 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.ГЇВїВЅ In contrast to the first three books on Ramanujan`s Lost Notebook, the fourth book does not focus on q-series.

Автор: Ramanujan
Название: Collected Papers of Srinivasa Ramanujan
ISBN: 1107536510 ISBN-13(EAN): 9781107536517
Издательство: Cambridge Academ
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Описание: Originally published in 1927, this book presents the collected papers of the renowned Indian mathematician Srinivasa Ramanujan (1887-1920), with editorial contributions from G. H. Hardy (1877-1947). Detailed notes are incorporated throughout and appendices are also included.

Автор: Ono, Ken Aczel, Amir D.
Название: My search for ramanujan
ISBN: 3319255665 ISBN-13(EAN): 9783319255668
Издательство: Springer
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Описание: Covering the life and enduring impact of the late mathematical prodigy Srinivasa Ramanujan and the influence he had on the life and career of Ken Ono, this book presents a powerful biographical diptych of two great mathematicians.
Ono was inspired to become a mathematician from the life and scientific quests of Ramanujan; Ramanujan's story guided Ono throughout his life, giving him hope when he needed it most. Although they never met, Ono believes a letter sent from Ramanujan's widow to his father, then a prominent Japanese mathematician, was a sign. This was the beginning of Ono's mission to carry on Ramanujan's legacy, and to develop Ramanujan's ideas within the context of modern mathematics.
Since then, Ono has spent his academic life trying to solve the mysteries that G.H. Hardy, one of the greatest English mathematicians of the 20th century, and others could not unravel: to find how Ramanujan came to his mathematical truths (which he claimed the Indian goddess Namagiri would tell him in dreams). In this way, Ono retraces the steps of Ramanujan's life throughout his career, drawing inspiration and strength for his own life from the travails and ultimate triumphs of his predecessor's brilliant, but tragically short, career.

Автор: Bruce C. Berndt
Название: Ramanujan`s Notebooks
ISBN: 1461269636 ISBN-13(EAN): 9781461269632
Издательство: Springer
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Описание: 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.

Автор: Bruce C. Berndt
Название: Ramanujan`s Notebooks
ISBN: 1461269326 ISBN-13(EAN): 9781461269328
Издательство: Springer
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Описание: 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.

Автор: Bruce C. Berndt
Название: Ramanujan`s Notebooks
ISBN: 1461272211 ISBN-13(EAN): 9781461272212
Издательство: Springer
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Описание: 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.

Автор: George E. Andrews; Bruce C. Berndt
Название: Ramanujan`s Lost Notebook
ISBN: 1441926666 ISBN-13(EAN): 9781441926661
Издательство: Springer
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Описание: "Ramanujan`s 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.

Автор: Bruce C. Berndt
Название: Ramanujan`s Notebooks
ISBN: 1461270073 ISBN-13(EAN): 9781461270072
Издательство: Springer
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Описание: Srinivasa Ramanujan is, arguably, the greatest mathematicianthat India has produced. He died very young, at the age of 32,leaving behind three notebooks containing almost 3000theorems, virtually all without proof. Hardy andothers strongly urged that notebooks be edited andpublished, and the result is this series of books.

Автор: Bruce C. Berndt
Название: Ramanujan`s Notebooks
ISBN: 1461288657 ISBN-13(EAN): 9781461288657
Издательство: Springer
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Описание: During the years 1903-1914, Ramanujan recorded many of his mathematical discoveries in notebooks without providing proofs. Part I, published in 1985, contains an account of Chapters 1-9 in the second notebook as well as a description of Ramanujan`s quarterly reports. In this volume, we examine Chapters 10-15 in Ramanujan`s second notebook.

Автор: Shaun Cooper
Название: Ramanujan`s Theta Functions
ISBN: 3319561715 ISBN-13(EAN): 9783319561714
Издательство: Springer
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Описание: Preface.- 0. Sum to Product Identities.- 1. Elliptic Functions.- 2. Transformations.- 3. Theta Functions.- 4. Levels 1, 2, 3, and 4: Jacobi's Inversion Theorem and Ramanujan's Alternative Theories.- 5. Level 5: The Rogers-Ramanujan Continued Fraction.- 6. Level 6: Ramanujan's Cubic Continued Fraction.- 7. Level 7.- 8. Level 8: The Ramanujan-Gollnitz-Gordon Continued Fraction.- 9. Level 9.- 10. Level 10: Ramanujan's Function k.- 11. Levels 11 and 23.- 12. Level 12.- 13. Hypergeometric Modular Transformations.- 14. Ramanujan's Series for 1/pi.- References.