Ramanujans Notebooks: Part I [Paperback]

Srinivasa Ramanujan is, arguably, the greatest mathematicianthat India has produced. His story is quite unusual:although he had no formal education inmathematics, hetaught himself, and managed to produce many important newresults. With the support of the English number theorist G.H. Hardy, Ramanujan received a scholarship to go to Englandand study mathematics. He died very young, at the age of 32,leaving behind three notebooks containing almost 3000theorems, virtually all without proof. G. H. Hardy andothers strongly urged that notebooks be edited andpublished, and the result is this series of books. Thisvolume dealswith Chapters 1-9 of Book II; each theorem iseither proved, or a reference to a proof is given.Srinivasa Ramanujan is, arguably, the greatest mathematicianthat India has produced. His story is quite unusual:although he had no formal education inmathematics, hetaught himself, and managed to produce many important newresults. With the support of the English number theorist G.H. Hardy, Ramanujan received a scholarship to go to Englandand study mathematics. He died very young, at the age of 32,leaving behind three notebooks containing almost 3000theorems, virtually all without proof. G. H. Hardy andothers strongly urged that notebooks be edited andpublished, and the result is this series of books. Thisvolume dealswith Chapters 1-9 of Book II; each theorem iseither proved, or a reference to a proof is given.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 Ramanujans Theory of Divergent Series.- 7 Sums of Powers, Bernoulli Numbers, and the Gamma function.- 8 Analogues of the Gamma function.- 9 Infinite Series Identities, Transforl£§