國立高雄大學圖資館 |

語系: 繁體中文

說明(常見問題)

圖資館首頁

登入

回首頁 到查詢結果 [ subject:"Ramanujan Aiyangar, Srinivasa," ]

切換: 標籤 | MARC模式 | ISBD

Ramanujan's lost notebook.Part V

Andrews, George E.

Ramanujan's lost notebook.Part V

紀錄類型:	書目-電子資源 : 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$q(electronic bk.)

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$q(electronic bk.)

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

567473
Ramanujan Aiyangar, Srinivasa,
1887-1920.Subjects--Topical Terms:

184409
Mathematics.

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

Dewey Class. No.: 510

Ramanujan's lost notebook.Part V
LDR:03826nmm a2200325 a 4500 001 543997
003 DE-He213
005 20190304104212.0
006 m d
007 cr nn 008maaau
008 190430s2018 gw s 0 eng d
020 $a 9783319778341$q(electronic bk.)
020 $a 9783319778327$q(paper)
024 7 $a 10.1007/978-3-319-77834-1 $2 doi
035 $a 978-3-319-77834-1
040 $a GP $c GP
041 0 $a eng
050 4 $a QA29.R3 $b A537 2018
072 7 $a PBKF $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBKF $2 thema
082 0 4 $a 510 $2 23
090 $a QA29.R3 $b A566 2018
100 1 $a Andrews, George E. $3 348623
245 1 0 $a Ramanujan's lost notebook. $n Part V $h [electronic resource] / $c by George E. Andrews, Bruce C. Berndt.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a xii, 430 p. : $b ill., digital ; $c 24 cm.
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.
600 1 0 $a Ramanujan Aiyangar, Srinivasa, $d 1887-1920. $3 567473
650 0 $a Mathematics. $3 184409
650 0 $a Mathematical analysis. $3 186133
650 0 $a Number theory. $3 189521
650 0 $a Mathematicians $z India $v Biography. $3 567474
650 1 4 $a Special Functions. $3 274846
650 2 4 $a Functions of a Complex Variable. $3 275780
650 2 4 $a Number Theory. $3 274059
700 1 $a Berndt, Bruce C. $3 348622
710 2 $a SpringerLink (Online service) $3 273601
773 0 $t Springer eBooks
856 4 0 $u https://doi.org/10.1007/978-3-319-77834-1
950 $a Mathematics and Statistics (Springer-11649)