Description
Springer Ramanujans Notebooks Part I by Bruce C. Berndt
Srinivasa Ramanujan is, arguably, the greatest mathematician_x000D_that India has produced. His story is quite unusual:_x000D_although he had no formal education inmathematics, he_x000D_taught himself, and managed to produce many important new_x000D_results. With the support of the English number theorist G._x000D_H. Hardy, Ramanujan received a scholarship to go to England_x000D_and study mathematics. He died very young, at the age of 32,_x000D_leaving behind three notebooks containing almost 3000_x000D_theorems, virtually all without proof. G. H. Hardy and_x000D_others strongly urged that notebooks be edited and_x000D_published, and the result is this series of books. This_x000D_volume dealswith Chapters 1-9 of Book II; each theorem is_x000D_either proved, or a reference to a proof is given._x000D_ Table of contents : - _x000D_
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._x000D_