Ramanujan's Lost Notebook : Part V. 1st ed. 2018

種類:

電子ブック

責任表示:

by George E. Andrews, Bruce C. Berndt

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2018

著者名:

• Andrews, George E.
• Berndt, Bruce C.
• SpringerLink (Online service)

ISBN:

9783319778341 [331977834X]    

注記:

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 Vol
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 deligh

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