Ramanujan’s Notebooks: Part I, Partie 1Springer Science & Business Media, 6 déc. 2012 - 357 pages 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. |
Table des matières
Sums of Powers Bernoulli Numbers and the Gamma Function | 150 |
Analogues of the Gamma Function | 181 |
CHAPTER 9 | 204 |
Infinite Series Identities Transformations and Evaluations | 232 |
Ramanujans Quarterly Reports | 295 |
References | 337 |
| 353 | |
Autres éditions - Tout afficher
Ramanujan's Notebooks, Partie 1 Srinivasa Ramanujan Aiyangar,Bruce C. Berndt Aucun aperçu disponible - 1985 |
Expressions et termes fréquents
A₁ Abramowitz and Stegun analytic continuation apply Entry asymptotic series Bell polynomials Bernoulli numbers c₁ calculation Chapter complete the proof complex number converges corollary to Entry cos(nx deduce defined derived desired equality desired result divergent series employ Entry 13 Entry 2(i Equating coefficients Euler-Maclaurin formula Euler-Maclaurin summation formula Example gamma function given by Ramanujan Hardy Hence hypotheses inversion left side Lemma Letting n tend Log² Log³ Maclaurin series magic squares Master Theorem Math Mathematical multiple natural number nonnegative integer notation obtain paper polynomials positive integer proof of Entry quarterly reports Ramanujan gives Ramanujan's proof Ramanujan's theory readily real number replaced result follows Riemann zeta-function right side S₁ second notebook Section Stirling's formula tends to oo valid values von Staudt-Clausen theorem Σ Α Σ Σ