Geschichte 1900-1920
Berndt
Bruce C.
Bruce C. Berndt
1939
Mathematical analysis
London
9780387777658
0387777652
New York
2005-
9780387255293
038725529X
9781461440802
1461440807
Springer
9781461438106
1461438101
2018-06-10
Mathematics
Andrews
George E.
George E. Andrews
1938
Mathematicians--India
Mathematicians
9780387281247
038728124X
en
2005/9999
60320109
60320109
2005/
Biography
This volume is the first of approximately four volumes devoted to providing statements, proofs, and discussions of all the claims made by Srinivasa Ramanujan in his lost notebook and all his other manuscripts and letters published with the lost notebook. In addition to the lost notebook, this publication contains copies of unpublished manuscripts in the Oxford library, in particular, his famous unpublished manuscript on the partition and tau-functions; fragments of both published and unpublished papers; miscellaneous sheets; and Ramanujan's letters to G. H. Hardy, written from nursing homes during Ramanujan's final two years in England. This volume contains accounts of 442 entries (counting multiplicities) made by Ramanujan in the aforementioned publication. The present authors have organized these claims into eighteen chapters, containing anywhere from two entries in Chapter 13 to sixty-one entries in Chapter 17. Most of the results contained in Ramanujan's Lost Notebook fall under the purview of q-series. These include mock theta functions, theta functions, partial theta function expansions, false theta functions, identities connected with the Rogers-Fine identity, several results in the theory of partitions, Eisenstein series, modular equations, the Rogers-Ramanujan continued fraction, other q-continued fractions, asymptotic expansions of q-series and q-continued fractions, integrals of theta functions, integrals of q-products, and incomplete elliptic integrals. Other continued fractions, other integrals, infinite series identities, Dirichlet series, approximations, arithmetic functions, numerical calculations, diophantine equations, and elementary mathematics are some of the further topics examined by Ramanujan in his lost notebook.
Ramanujan's lost notebook
9780387777665
0387777660
9781461438090
1461438098
Ramanujan Aiyangar
Srinivasa
Srinivasa Ramanujan Aiyangar
1887
1920
9781461440819
1461440815
India.
nyu
Ramanujan Aiyangar
Srinivasa
Srinivasa Ramanujan Aiyangar
1887
1920
Q.-Serie
Number theory