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Ramanujan's lost notebook.. Part V

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Ramanujan's lost notebook./ by George E. Andrews, Bruce C. Berndt.
作者:	Andrews, George E.
其他作者:	Berndt, Bruce C.
出版者:	Cham :Springer International Publishing : : 2018.,
面頁冊數:	xii, 430 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
標題:	Mathematics. -
電子資源:	https://doi.org/10.1007/978-3-319-77834-1
ISBN:	9783319778341

Ramanujan's lost notebook.. Part V
Andrews, George E.

Ramanujan's lost notebook.Part V[electronic resource] /by George E. Andrews, Bruce C. Berndt. - Cham :Springer International Publishing :2018. - xii, 430 p. :ill., digital ;24 cm.

Preface -- 1. Introduction -- 2. Third Order Mock Theta Functions: Elementary Identities -- 3. Fifth Order Mock Theta Functions: Elementary Identities -- 4. Third Order Mock Theta Functions: Partial Fraction Expansions -- 5. The Mock Theta Conjectures: Equivalence -- 6. Fifth Order Mock Theta Functions: Proof of the Mock Theta Conjectures -- 7. Sixth Order Mock Theta Functions -- 8. Tenth Order Mock Theta Functions. Part I, The First Four Identities -- 9. Tenth Order Mock Theta Functions: Part II, Identities for phi10(q), psi10(q) -- 10. Tenth Order Mock Theta Functions: Part III, Identities for ch10(q), kh10(q) -- 11. Tenth Order Mock Theta Functions. Part IV -- 12. Transformation Formulas: 10th Order Mock Theta Functions -- 13. Two Identities Involving a Mordell Integral and Appel-Lerch Sums -- 14. Ramanujan's Last Letter to Hardy -- 15. Euler Products in Ramanujan's Lost Notebook -- 16. Continued Fractions -- 17. Recent Work on Mock Theta Functions -- 18. Commentary on and Corrections to the First Four Volumes -- 19. The Continuing Mystery -- Location Guide -- Provenance -- References -- Index.

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 fifth and final installment of the authors' examination of Ramanujan's lost notebook focuses on the mock theta functions first introduced in Ramanujan's famous Last Letter. This volume proves all of the assertions about mock theta functions in the lost notebook and in the Last Letter, particularly the celebrated mock theta conjectures. Other topics feature Ramanujan's many elegant Euler products and the remaining entries on continued fractions not discussed in the preceding volumes. 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.

ISBN: 9783319778341

Standard No.: 10.1007/978-3-319-77834-1doiSubjects--Personal Names:

884930
Ramanujan Aiyangar, Srinivasa,
1887-1920.Subjects--Topical Terms:

527692
Mathematics.

LC Class. No.: QA29.R3 / A537 2018

Dewey Class. No.: 510

Ramanujan's lost notebook.. Part V
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505 0 $a Preface -- 1. Introduction -- 2. Third Order Mock Theta Functions: Elementary Identities -- 3. Fifth Order Mock Theta Functions: Elementary Identities -- 4. Third Order Mock Theta Functions: Partial Fraction Expansions -- 5. The Mock Theta Conjectures: Equivalence -- 6. Fifth Order Mock Theta Functions: Proof of the Mock Theta Conjectures -- 7. Sixth Order Mock Theta Functions -- 8. Tenth Order Mock Theta Functions. Part I, The First Four Identities -- 9. Tenth Order Mock Theta Functions: Part II, Identities for phi10(q), psi10(q) -- 10. Tenth Order Mock Theta Functions: Part III, Identities for ch10(q), kh10(q) -- 11. Tenth Order Mock Theta Functions. Part IV -- 12. Transformation Formulas: 10th Order Mock Theta Functions -- 13. Two Identities Involving a Mordell Integral and Appel-Lerch Sums -- 14. Ramanujan's Last Letter to Hardy -- 15. Euler Products in Ramanujan's Lost Notebook -- 16. Continued Fractions -- 17. Recent Work on Mock Theta Functions -- 18. Commentary on and Corrections to the First Four Volumes -- 19. The Continuing Mystery -- Location Guide -- Provenance -- References -- Index.
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 fifth and final installment of the authors' examination of Ramanujan's lost notebook focuses on the mock theta functions first introduced in Ramanujan's famous Last Letter. This volume proves all of the assertions about mock theta functions in the lost notebook and in the Last Letter, particularly the celebrated mock theta conjectures. Other topics feature Ramanujan's many elegant Euler products and the remaining entries on continued fractions not discussed in the preceding volumes. 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.
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