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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.
List 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.
Summary
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.
