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| POSSEDUTO (se manca la collocazione vai al documento contenente) | |
| Autore principale: | Ferraro, Giovanni.
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| Titolo: | The rise and development of the theory of series up to the early 1820s / Giovanni Ferraro. |
| Pubblicazione: | New York : Springer, c2008. |
| Descrizione fisica: | XV, 389 p. ; 25 cm |
| Serie: | Sources and studies in the history of mathematics and physical sciences |
| Contiene: | Indice: Pt. 1. From the beginnings of the 17th century to about 1720: convergence and formal manipulation: 1. Series before the rise of the calculus 2. Geometrical quantities and series in Leibniz 3. The Bernoulli series and Leibniz's analogy 4. Newton's method of series 5. Jacob Bernoulli's treatise on series 6. The Taylor series 7. Quantities and their representations 8. The formal-quantitative theory of series 9. The first appearance of divergent series. Pt. 2. From the 1720s to the 1760s: the development of a more formal conception: 10. De Moivre's recurrent series and Bernoulli's method 11. Acceleration of series and Stirling's series 12. Maclaurin's contribution 13. The young Euler between innovation and tradition 14. Euler's derivation of the Euler-Maclaurin summation formula 15. On the sum of an asymptotic series 16. Infinite products and continued fractions 17. Series and number theory 18. Analysis after the 1740s 19. The formal concept of series. Pt. 3. The theory of series after 1760: successes and problems of the triumphant formalism: 20. Lagrange inversion theorem 21. Toward the calculus of operations 22. Laplace's calculus of generating functions 23. The problem of analytical representation of nonelementary quantities 24. Inexplicable functions 25. Integration and functions 26. Series and differential equations 27. Trigonometric series 28. Further developments of the formal theory of series 29. Attempts to introduce new transcendental functions 30. D'Alembert and Lagrange and the inequality technique. Pt. 4. The decline of the formal theory of series: 31. Fourier and Fourier series 32. Gauss and the hypergeometric series 33. Cauchy's rejection of the 18th-century theory of series. References. Author index. Subject index |
| ISBN: | 9780387734675 |
| Discipline: | Analisi matematica--Studi. |
| Sudd. cronologiche: | Secolo XVIII. Secolo XIX. |
| Collocazione: | LS 16922 |
| Nota di esemplare: | Mostra nota di esemplare |
| 000000967297 |
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