Ramanujan's lost notebook. Part IV
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 des...
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| Formato: | Livre numérique |
| Idioma: | Anglais |
| Publicado em: |
Cham :
Springer International Publishing
2013.
Cham : Springer Nature |
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| Acesso em linha: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
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Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) Type of computer file: Fichier EPUB |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Ramanujan's lost notebook, Part IV, [edited by] George E. Andrews, Bruce C. Berndt., 2013, New York, Springer, 1 vol. (XVII-439 p.), 978-1-4614-4080-2 |
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| 020 | |a 9781461440819 | ||
| 041 | 0 | |a eng | |
| 082 | |a 512.7 | ||
| 084 | |a 11M06. 2010 | ||
| 084 | |a 11J17. 2010 | ||
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| 100 | 1 | |a Ramanujan, Srinivasa, |d 1887-1920, |c mathématicien. | |
| 245 | 1 | 0 | |a Ramanujan's lost notebook. |n Part IV |c George E. Andrews, Bruce C. Berndt. |
| 260 | |a Cham : |b Springer International Publishing. | ||
| 260 | |a Cham : |b Springer Nature, |c 2013. | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Type of computer file: Fichier EPUB | ||
| 504 | |a Bibliogr. p. 421-434 de l'édition imprimée. Index | ||
| 505 | 0 | |a Preface -- 1 Introduction.- 2 Double Series of Bessel Functions and the Circle and Divisor Problems.- 3 Koshliakov's Formula and Guinand's Formula.- 4 Theorems Featuring the Gamma Function.- 5 Hypergeometric Series.- 6 Euler's Constant.- 7 Problems in Diophantine Approximation.- 8 Number Theory.- 9 Divisor Sums -- 10 Identities Related to the Riemann Zeta Function and Periodic Zeta Functions -- 11 Two Partial Unpublished Manuscripts on Sums Involving Primes.- 12 Infinite Series -- 13 A Partial Manuscript on Fourier and Laplace Transforms -- 14 Integral Analogues of Theta Functions adn Gauss Sums -- 15 Functional Equations for Products of Mellin Transforms -- 16 Infinite Products -- 17 A Preliminary Version of Ramanujan's Paper, On the Integral S_0^x tan^(-1)t)/t dt -- 18 A Partial Manuscript Connected with Ramanujan's Paper, Some Definite Integrals.- 19 Miscellaneous Results in Analysis -- 20 Elementary Results -- 21 A Strange, Enigmatic Partial Manuscript.- Location Guide -- Provenance -- References -- Index | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 538 | |a Accès Internet, nécessite un lecteur de fichier EPUB | ||
| 650 | |a Nombres, Théorie des | ||
| 650 | |a Analyse mathématique | ||
| 700 | 1 | |a Andrews, George E., |d 1938- |4 edt | |
| 700 | 1 | |a Berndt, Bruce Carl, |d 1939- |4 edt | |
| 776 | 0 | |0 170672123 |t Ramanujan's lost notebook |h Part IV |f [edited by] George E. Andrews, Bruce C. Berndt. |d 2013 |c New York |n Springer |p 1 vol. (XVII-439 p.) |z 978-1-4614-4080-2 | |
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