Ferraro, Giovanni
The Rise and Development of the Theory of Series up to the Early 1820s
Part I. From the beginnings of the 17th century to about 1720: Convergence and formal manipulation
1. Series before the rise of the calculus
Giovanni Ferraro
2. Geometrical quantities and series in Leibniz
Giovanni Ferraro
3. The Bernoulli series and Leibniz’s analogy
Giovanni Ferraro
4. Newton’s method of series
Giovanni Ferraro
5. Jacob Bernoulli’s treatise on series
Giovanni Ferraro
6. The Taylor series
Giovanni Ferraro
7. Quantities and their representations
Giovanni Ferraro
8. The formal-quantitative theory of series
Giovanni Ferraro
9. The first appearance of divergent series
Giovanni Ferraro
Part II. From the 1720s to the 1760s: The development of a more formal conception
10. De Moivre’s recurrent series and Bernoulli’s method
Giovanni Ferraro
11. Acceleration of series and Stirling’s series
Giovanni Ferraro
12. Maclaurin’s contribution
Giovanni Ferraro
13. The young Euler between innovation and tradition
Giovanni Ferraro
14. Euler’s derivation of the Euler–Maclaurin summation formula
Giovanni Ferraro
15. On the sum of an asymptotic series
Giovanni Ferraro
16. Infinite products and continued fractions
Giovanni Ferraro
17. Series and number theory
Giovanni Ferraro
18. Analysis after the 1740s
Giovanni Ferraro
19. The formal concept of series
Giovanni Ferraro
Part III. The theory of series after 1760: Successes and problems of the triumphant formalism
20. Lagrange inversion theorem
Giovanni Ferraro
21. Toward the calculus of operations
Giovanni Ferraro
22. Laplace’s calculus of generating functions
Giovanni Ferraro
23. The problem of analytical representation of nonelementary quantities
Giovanni Ferraro
24. Inexplicable functions
Giovanni Ferraro
25. Integration and functions
Giovanni Ferraro
26. Series and differential equations
Giovanni Ferraro
27. Trigonometric series
Giovanni Ferraro
28. Further developments of the formal theory of series
Giovanni Ferraro
29. Attempts to introduce new transcendental functions
Giovanni Ferraro
30. D’Alembert and Lagrange and the inequality technique
Giovanni Ferraro
Part IV. The decline of the formal theory of series
31. Fourier and Fourier series
Giovanni Ferraro
32. Gauss and the hypergeometric series
Giovanni Ferraro
33. Cauchy’s rejection of the 18th-century theory of series
Giovanni Ferraro
DRM-restrictions
Printing: not available
Clipboard copying: not available
Keywords: MATHEMATICS / General MAT000000
- Author(s)
- Ferraro, Giovanni
- Publisher
- Springer
- Publication year
- 2008
- Language
- en
- Edition
- 1
- Category
- Natural Sciences
- Format
- Ebook
- eISBN (PDF)
- 9780387734682