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.

Produktinformation

Utgivningsdatum:2018-09-18
Mått:155 x 235 x 36 mm
Vikt:818 g
Format:Inbunden
Språk:Engelska
Antal sidor:430
Förlag:Springer International Publishing AG
ISBN:9783319778327

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George E. Andrews is currently a professor of mathematics at Pennsylvania State University. Bruce C. Berndt is currently a professor of mathematics at the University of Illinois.

Innehållsförteckning

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 Correctionsto the First Four Volumes.- 19. The Continuing Mystery.- Location Guide.- Provenance.- References.- Index.