The Rise and Development of the Theory of Series up to the Early 1820s
The theory of series in the 17th and 18th centuries poses several interesting problems to historians. Most of the results derived from this time were derived using methods which would be found unacceptable today, and as a result, when one looks back to the theory of series prior to Cauchy without re...
Guardat en:
| Autor principal: | |
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| Format: | Livre numérique |
| Idioma: | Anglais |
| Publicat: |
New York, NY :
Springer New York
[20..].
Cham : Springer Nature |
| Edició: | 1st ed. 2008. |
| Col·lecció: | Sources and Studies in the History of Mathematics and Physical Sciences
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| Matèries: | |
| Accés en línia: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Nota: |
L'impression du document génère 388 p. Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • The Rise and Development of the Theory of Series up to the Early 1820s, Texte imprimé, 9780387520087 • The rise and development of the theory of series up to the early 1820s, Giovanni Ferraro, 2008, New York, NY, Springer, 1 vol. (xv-389 p.), Sources and studies in the history of mathematics and physical sciences, 978-0-387-73467-5 • The rise and development of the theory of series up to the early 1820s, Giovanni Ferraro, 2008, New York, NY, Springer, 1 vol. (xv-389 p.), Sources and studies in the history of mathematics and physical sciences, 978-0-387-73467-5 |
Taula de continguts:
- From the beginnings of the 17th century to about 1720: Convergence and formal manipulation Series before the rise of the calculus Geometrical quantities and series in Leibniz The Bernoulli series and Leibniz's analogy Newton's method of series Jacob Bernoulli's treatise on series The Taylor series Quantities and their representations The formal-quantitative theory of series The first appearance of divergent series From the 1720s to the 1760s: The development of a more formal conception De Moivre's recurrent series and Bernoulli's method Acceleration of series and Stirling's series Maclaurin's contribution The young Euler between innovation and tradition Euler's derivation of the Euler-Maclaurin summation formula On the sum of an asymptotic series Infinite products and continued fractions Series and number theory Analysis after the 1740s The formal concept of series The theory of series after 1760: Successes and problems of the triumphant formalism Lagrange inversion theorem Toward the calculus of operations Laplace's calculus of generating functions The problem of analytical representation of nonelementary quantities Inexplicable functions Integration and functions Series and differential equations Trigonometric series Further developments of the formal theory of series Attempts to introduce new transcendental functions D'Alembert and Lagrange and the inequality technique The decline of the formal theory of series Fourier and Fourier series Gauss and the hypergeometric series Cauchy's rejection of the 18th-century theory of series.