Ramanujan's Notebooks: Part I

by Bruce C. Berndt

Overview

Srinivasa Ramanujan is, arguably, the greatest mathematician that India has produced. His story is quite unusual: although he had no formal education inmathematics, he taught himself, and managed to produce many important new results. With the support of the English number theorist G. H. Hardy, Ramanujan received a scholarship to go to England and study mathematics. He died very young, at the age of 32, leaving behind three notebooks containing almost 3000 theorems, virtually all without proof. G. H. Hardy and others strongly urged that notebooks be edited and published, and the result is this series of books. This volume dealswith Chapters 1-9 of Book II; each theorem is either proved, or a reference to a proof is given.

Product Details

ISBN-13:	9780387961101
Publisher:	Springer New York
Publication date:	03/12/1985
Edition description:	1985
Pages:	357
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

1 Magic Squares.- 2 Sums Related to the Harmonic Series or the Inverse Tangent function.- 3 Combinatorial Analysis and Series Inversions.- 4 Iterates of the Exponential Function and an Ingenious Formal Technique.- 5 Eulerian Polynomials and Numbers, Bernoulli Numbers, and the Riemann Zeta-Function.- 6 Ramanujan’s Theory of Divergent Series.- 7 Sums of Powers, Bernoulli Numbers, and the Gamma function.- 8 Analogues of the Gamma function.- 9 Infinite Series Identities, Transformations, and Evaluations.- Ramanujan’s Quarterly Reports.- References.

Editorial Reviews

"Ramanujan studies" have recently--and happily--become something of an industry; several mathematicians are presently devoting their professional energy to the explication of inspired insight and unearthly beauty long buried in Ramanujan's notebooks (themselves recently published, in photo-facsimile, for the first time). The present volume represents the continuation of a projected four-part series, by a mathematician associated with the University of Illinois. In six chapters it treats notebook entries pertaining to hypergeometric series, continued fractions, integrals and asymptotic expansions, infinite series, asymptotic expansions and modular forms. Chapters begin with an introductory essay, followed by notebook entries, proofs, corollaries and remarks, an overall objective being to detect and expose the pattern of Ramanujan's argument (at this point still frequently elusive). (NW) Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews