An Invitation To The Rogers Ramanujan Identities
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An Invitation To The Rogers Ramanujan Identities
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Author : Andrew V. Sills
language : en
Publisher: CRC Press
Release Date : 2017-10-16
An Invitation To The Rogers Ramanujan Identities written by Andrew V. Sills and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-10-16 with Mathematics categories.
The Rogers--Ramanujan identities are a pair of infinite series—infinite product identities that were first discovered in 1894. Over the past several decades these identities, and identities of similar type, have found applications in number theory, combinatorics, Lie algebra and vertex operator algebra theory, physics (especially statistical mechanics), and computer science (especially algorithmic proof theory). Presented in a coherant and clear way, this will be the first book entirely devoted to the Rogers—Ramanujan identities and will include related historical material that is unavailable elsewhere.
An Invitation To Q Series
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Author : Hei-Chi Chan
language : en
Publisher: World Scientific
Release Date : 2011
An Invitation To Q Series written by Hei-Chi Chan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
The aim of this lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan. Two central results in these notes are: (1) the evaluation of the Rogers–Ramanujan continued fraction — a result that convinced G H Hardy that Ramanujan was a “mathematician of the highest class”, and (2) what G H Hardy called Ramanujan's “Most Beautiful Identity”. This book covers a range of related results, such as several proofs of the famous Rogers–Ramanujan identities and a detailed account of Ramanujan's congruences. It also covers a range of techniques in q-series.
An Invitation To Q Series
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Author : Chan Hei-Chi
language : en
Publisher:
Release Date : 2011
An Invitation To Q Series written by Chan Hei-Chi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with q-series categories.
Invitation To Q Series An From Jacobi S Triple Product Identity To Ramanujan S Most Beautiful Identity
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Author : Hei-chi Chan
language : en
Publisher: World Scientific
Release Date : 2011-04-04
Invitation To Q Series An From Jacobi S Triple Product Identity To Ramanujan S Most Beautiful Identity written by Hei-chi Chan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04-04 with Mathematics categories.
The aim of these lecture notes is to provide a self-contained exposition of several fascinating formulas discovered by Srinivasa Ramanujan. Two central results in these notes are: (1) the evaluation of the Rogers-Ramanujan continued fraction — a result that convinced G H Hardy that Ramanujan was a “mathematician of the highest class”, and (2) what G. H. Hardy called Ramanujan's “Most Beautiful Identity”. This book covers a range of related results, such as several proofs of the famous Rogers-Ramanujan identities and a detailed account of Ramanujan's congruences. It also covers a range of techniques in q-series.
An Introduction To Q Analysis
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Author : Warren P. Johnson
language : en
Publisher: American Mathematical Soc.
Release Date : 2020-10-06
An Introduction To Q Analysis written by Warren P. Johnson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-06 with Education categories.
Starting from simple generalizations of factorials and binomial coefficients, this book gives a friendly and accessible introduction to q q-analysis, a subject consisting primarily of identities between certain kinds of series and products. Many applications of these identities to combinatorics and number theory are developed in detail. There are numerous exercises to help students appreciate the beauty and power of the ideas, and the history of the subject is kept consistently in view. The book has few prerequisites beyond calculus. It is well suited to a capstone course, or for self-study in combinatorics or classical analysis. Ph.D. students and research mathematicians will also find it useful as a reference.
Ramanujan S Place In The World Of Mathematics
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Author : Krishnaswami Alladi
language : en
Publisher: Springer Nature
Release Date : 2021-09-17
Ramanujan S Place In The World Of Mathematics written by Krishnaswami Alladi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-17 with Mathematics categories.
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.
Q Series With Applications To Combinatorics Number Theory And Physics
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Author : Bruce C. Berndt
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Q Series With Applications To Combinatorics Number Theory And Physics written by Bruce C. Berndt and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
The subject of $q$-series can be said to begin with Euler and his pentagonal number theorem. In fact, $q$-series are sometimes called Eulerian series. Contributions were made by Gauss, Jacobi, and Cauchy, but the first attempt at a systematic development, especially from the point of view of studying series with the products in the summands, was made by E. Heine in 1847. In the latter part of the nineteenth and in the early part of the twentieth centuries, two Englishmathematicians, L. J. Rogers and F. H. Jackson, made fundamental contributions. In 1940, G. H. Hardy described what we now call Ramanujan's famous $ 1\psi 1$ summation theorem as ``a remarkable formula with many parameters.'' This is now one of the fundamental theorems of the subject. Despite humble beginnings,the subject of $q$-series has flourished in the past three decades, particularly with its applications to combinatorics, number theory, and physics. During the year 2000, the University of Illinois embraced The Millennial Year in Number Theory. One of the events that year was the conference $q$-Series with Applications to Combinatorics, Number Theory, and Physics. This event gathered mathematicians from the world over to lecture and discuss their research. This volume presents nineteen of thepapers presented at the conference. The excellent lectures that are included chart pathways into the future and survey the numerous applications of $q$-series to combinatorics, number theory, and physics.
My Search For Ramanujan
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Author : Ken Ono
language : en
Publisher: Springer
Release Date : 2016-04-20
My Search For Ramanujan written by Ken Ono and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-20 with Mathematics categories.
"The son of a prominent Japanese mathematician who came to the United States after World War II, Ken Ono was raised on a diet of high expectations and little praise. Rebelling against his pressure-cooker of a life, Ken determined to drop out of high school to follow his own path. To obtain his father’s approval, he invoked the biography of the famous Indian mathematical prodigy Srinivasa Ramanujan, whom his father revered, who had twice flunked out of college because of his single-minded devotion to mathematics. Ono describes his rocky path through college and graduate school, interweaving Ramanujan’s story with his own and telling how at key moments, he was inspired by Ramanujan and guided by mentors who encouraged him to pursue his interest in exploring Ramanujan’s mathematical legacy. Picking up where others left off, beginning with the great English mathematician G.H. Hardy, who brought Ramanujan to Cambridge in 1914, Ono has devoted his mathematical career to understanding how in his short life, Ramanujan was able to discover so many deep mathematical truths, which Ramanujan believed had been sent to him as visions from a Hindu goddess. And it was Ramanujan who was ultimately the source of reconciliation between Ono and his parents. Ono’s search for Ramanujan ranges over three continents and crosses paths with mathematicians whose lives span the globe and the entire twentieth century and beyond. Along the way, Ken made many fascinating discoveries. The most important and surprising one of all was his own humanity."
Who S Who In Technology Today
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Author :
language : en
Publisher:
Release Date : 1980
Who S Who In Technology Today written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Engineers categories.
Who S Who In Technology Today
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Author : Barbara A. Tinucci
language : en
Publisher:
Release Date : 1984
Who S Who In Technology Today written by Barbara A. Tinucci and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Engineers categories.