Divergent SeriesAmerican Mathematical Soc., 2000 - 396 pàgines From the Preface by J. E. Littlewood: "All [Hardy's] books gave him some degree of pleasure, but this one, his last, was his favourite. When embarking on it he told me that he believed in its value (as well he might), and also that he looked forward to the task with enthusiasm. He had actually given lectures on the subject at intervals ever since his return to Cambridge in 1931, and he had at one time or another lectured on everything in the book except Chapter XIII [TheEuler-MacLaurin sum formula] ... [I]n the early years of the century the subject [Divergent Series], while in no way mystical or unrigorous, was regarded as sensational, and about the present title, now colourless, there hung an aroma of paradox and audacity." |
Continguts
SOME HISTORICAL EXAMPLES | 23 |
GENERAL THEOREMS | 40 |
ARITHMETIC MEANS | 94 |
NOTES ON CHAPTER V | 118 |
TAUBERIAN THEOREMS FOR POWER SERIES | 148 |
THE METHODS OF EULER AND BOREL | 178 |
NOTES ON CHAPTER IX | 224 |
WIENERS TAUBERIAN THEOREMS | 283 |
THE EULERMACLAURIN SUM FORMULA | 318 |
ON THE EVALUATION or CERTAIN DEFINITE INTEGRALS | 349 |
ON RIEMANN AND ABEL SUMMABILITY | 365 |
Two THEOREMS OF M L OARTWRIGHT | 381 |
| 394 | |
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Frases i termes més freqüents
absolutely convergent analysis apply argument assertion assume asymptotic becomes Borel’s bounded calculations chapter choose circle complex concerning consider constant continuous convenient corresponding decreasing deduce defined definition depends divergent series equations equivalent Euler example Finally find finite first fixed follows formal formula function given gives Hardy Hence hypothesis implies important includes increases independent infinity integral interesting interval less limit means method multiplication natural necessary observed obtain origin particular plain plainly PLMS positive proof proof of Theorem prove THEOREM referred region regular remarks replace respectively result satisfied satisfy sense sequence similar similarly simple slowly sufficient summable summation suppose tends theory transformation true uniformly usually values write