Functions, functional relations, and the laws of continuity in Euler

DOI10.1006/hmat.2000.2278zbMath0979.01010OpenAlexW2034885407MaRDI QIDQ1578260

Giovanni Ferraro

Publication date: 22 February 2002

Published in: Historia Mathematica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/hmat.2000.2278

zbMATH Keywords

continuitydifferentiabilityfunctionvariable

Mathematics Subject Classification ID

History of mathematics in the 18th century (01A50)

Related Items (13)

Unnamed Item ⋮ Convergence and formal manipulation in the theory of series from 1730 to 1815 ⋮ Developing into series and returning from series: A note on the foundations of eighteenth-century analysis ⋮ Which notions of function were given by Euler? ⋮ Leonhard Euler's use and understanding of mathematical transcendence ⋮ Variables, limits, and infinitesimals in Portugal in the late 18th century. ⋮ Differentials and differential coefficients in the Eulerian foundations of the calculus. ⋮ The foundational aspects of Gauss's work on the hypergeometric, factorial and digamma functions ⋮ Geometry and analysis in Euler's integral calculus ⋮ Throwing Some Light on the Vast Darkness that is Analysis: Niels Henrik Abel's Critical Revision and the Concept of Absolute Convergence ⋮ Some aspects of Euler's theory of series: Inexplicable functions and the Euler-Maclaurin summation formula ⋮ Euler's beta integral in Pietro Mengoli's works ⋮ Lagrange's theory of analytical functions and his ideal of purity of method

Cites Work

• Quelques aspects de l'histoire des équations fonctionnelles liées à l'évolution du concept de fonction. (Some aspects of the history of functional equations combined with the development of the of concept function)
• The calculus of the trigonometric functions
• The calculus as algebraic analysis: Some observations on mathematical analysis in the 18th century
• Differentials, higher-order differentials and the derivative in the Leibnizian calculus
• Some aspects of Euler's theory of series: Inexplicable functions and the Euler-Maclaurin summation formula
• The first modern definition of the sum of a divergent series: An aspect of the rise of 20th century mathematics
• Joseph Louis Lagrange's algebraic vision of the calculus
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