000			02176nam a22002057a 4500
003			OSt
005			20240910164307.0
008			190117b ||||| |||| 00| 0 eng d
020			_a9781493976256
040			_cTata Book House _aICTS-TIFR
050			_aQA29.R3
100			_aAndrews, George E.
245			_a Ramanujan's lost notebook _b: Part I
260			_aUSA: _bSpringer, _c[c2005]
300			_a437 p
505			_aIntroduction 1. Rogers-Ramanujan Continued Fraction and Its Modular Properties 2. Explicit Evaluations of the Rogers-Ramanujan Continued Fraction 3. A Fragment on the Rogers-Ramanujan and Cubic Continued Fractions 4. The Rogers-Ramanujan Continued Fraction and Its Connections with Partitions and Lambert Series 5. Finite Rogers-Ramanujan Continued Fractions 6. Other q-continued Fractions 7. Asymptotic Formulas for Continued Fractions 8. Ramanujan’s Continued Fraction for (q2;q3)∞/(q;q3)∞ 9. The Rogers-Fine Identity 10. An Empirical Study of the Rogers-Ramanujan Identities 11. Rogers-Ramanujan-Slater Type Identities 12. Partial Fractions 13. Hadamard Products for Two q-Series 14. Integrals of Theta Functions 15. Incomplete Elliptic Integrals 16. Infinite Integrals of q-Products 17. Modular Equations in Ramanujan’s Lost Notebook 18. Fragments on Lambert Series
520			_aThe "lost notebook" contains considerable material on mock theta functions and so undoubtedly emanates from the last year of Ramanujan's life. It should be emphasized that the material on mock theta functions is perhaps Ramanujan's deepest work. Mathematicians are probably several decades away from a complete understanding of those functions. More than half of the material in the book is on q-series, including mock theta functions; the remaining part deals with theta function identities, modular equations, incomplete elliptic integrals ofthe first kind and other integrals of theta functions, Eisenstein series, particular values of theta functions, the Rogers-Ramanujan continued fraction, other q-continued fractions, other integrals, and parts of Hecke's theory of modular forms.
700			_aBerndt, Bruce C.
942			_2lcc _cBK
999			_c2141 _d2141