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010			_a 2019743081
020			_a9781489991751
024	7		_a10.1007/978-3-319-77834-1 _2doi
035			_a(DE-He213)978-3-319-77834-1
040			_aDLC _beng _epn _erda _cDLC _dIIITD
072		7	_aMAT034000 _2bisacsh
072		7	_aPBKF _2bicssc
072		7	_aPBKF _2thema
082	0	4	_a515.984 _223 _bAND-R
100	1		_aAndrews, George E.
245	1	0	_aRamanujan's lost notebook : _bpart 4 _cby George E. Andrews and Bruce C. Berndt.
260			_aNew York : _bSpringer, _c©2013
300			_axvii, 439 p. : _bill. ; _c25 cm.
490			_aRamanujan's lost notebook
505	0		_aPreface -- 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			_aIn 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.
650		0	_aFunctions of complex variables.
650		0	_aNumber theory.
650		0	_aSpecial functions.
650	1	4	_aSpecial Functions.
650	2	4	_aFunctions of a Complex Variable.
650	2	4	_aNumber Theory.
700	1		_aBerndt, Bruce C.
776	0	8	_iPrint version: _tRamanujan's lost notebook _z9783319778327 _w(DLC) 2018935289
776	0	8	_iPrinted edition: _z9783030085506
776	0	8	_iPrinted edition: _z9783319778327
776	0	8	_iPrinted edition: _z9783319778334
906			_a0 _bibc _corigres _du _encip _f20 _gy-gencatlg
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999			_c171314 _d171314