New York
Springer
MATHEMATICS--Pre-Calculus
Andrews
George E.
George E. Andrews
1938
9780387255293
038725529X
Berndt
Bruce C.
Bruce C. Berndt
1939
2016-05-12
MATHEMATICS--Essays
London
9780387281247
038728124X
MATHEMATICS--Reference
2005
Ramanujan's lost notebook. Part I.
Print version:
Ramanujan Aiyangar
Srinivasa
Srinivasa Ramanujan Aiyangar
1887
1920
9781280308345
1280308346
Mathematics
Ramanujan Aiyangar
Srinivasa
Srinivasa Ramanujan Aiyangar
1887
1920
2005
Ramanujan's lost notebook. Part I
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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. The "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 of the 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.
The Rogers-Ramanujan Continued Fraction and Its Modular Properties -- Explicit Evaluations of the Rogers-Ramanujan Continued Fraction -- A Fragment on the Rogers-Ramanujan and Cubic Continued Fractions -- Rogers-Ramanujan Continued Fraction--Partitions, Lambert Series -- Finite Rogers-Ramanujan Continued Fractions -- Other q-continued Fractions -- Asymptotic Formulas for Continued Fractions -- Ramanujan's Continued Fraction for (q2; q3)[infinity]/(q; q3)[infinity] -- The Rogers-Fine Identity -- An Empirical Study of the Rogers-Ramanujan Identities -- Rogers-Ramanujan-Slater-Type Identities -- Partial Fractions -- Hadamard Products for Two q-Series -- Integrals of Theta Functions -- Incomplete Elliptic Integrals -- Infinite Integrals of q-Products -- Modular Equations in Ramanujan's Lost Notebook -- Fragments on Lambert Series.
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