↓ Skip to main content

The Rise and Development of the Theory of Series up to the Early 1820s

Overview of attention for book
Cover of 'The Rise and Development of the Theory of Series up to the Early 1820s'

Table of Contents

  1. Altmetric Badge
    Book Overview
  2. Altmetric Badge
    Chapter 1 Series before the rise of the calculus
  3. Altmetric Badge
    Chapter 2 Geometrical quantities and series in Leibniz
  4. Altmetric Badge
    Chapter 3 The Bernoulli series and Leibniz’s analogy
  5. Altmetric Badge
    Chapter 4 Newton’s method of series
  6. Altmetric Badge
    Chapter 5 Jacob Bernoulli’s treatise on series
  7. Altmetric Badge
    Chapter 6 The Taylor series
  8. Altmetric Badge
    Chapter 7 Quantities and their representations
  9. Altmetric Badge
    Chapter 8 The formal-quantitative theory of series
  10. Altmetric Badge
    Chapter 9 The first appearance of divergent series
  11. Altmetric Badge
    Chapter 10 De Moivre’s recurrent series and Bernoulli’s method
  12. Altmetric Badge
    Chapter 11 Acceleration of series and Stirling’s series
  13. Altmetric Badge
    Chapter 12 Maclaurin’s contribution
  14. Altmetric Badge
    Chapter 13 The young Euler between innovation and tradition
  15. Altmetric Badge
    Chapter 14 Euler’s derivation of the Euler–Maclaurin summation formula
  16. Altmetric Badge
    Chapter 15 On the sum of an asymptotic series
  17. Altmetric Badge
    Chapter 16 Infinite products and continued fractions
  18. Altmetric Badge
    Chapter 17 Series and number theory
  19. Altmetric Badge
    Chapter 18 Analysis after the 1740s
  20. Altmetric Badge
    Chapter 19 The formal concept of series
  21. Altmetric Badge
    Chapter 20 Lagrange inversion theorem
  22. Altmetric Badge
    Chapter 21 Toward the calculus of operations
  23. Altmetric Badge
    Chapter 22 Laplace’s calculus of generating functions
  24. Altmetric Badge
    Chapter 23 The problem of analytical representation of nonelementary quantities
  25. Altmetric Badge
    Chapter 24 Inexplicable functions
  26. Altmetric Badge
    Chapter 25 Integration and functions
  27. Altmetric Badge
    Chapter 26 Series and differential equations
  28. Altmetric Badge
    Chapter 27 Trigonometric series
  29. Altmetric Badge
    Chapter 28 Further developments of the formal theory of series
  30. Altmetric Badge
    Chapter 29 Attempts to introduce new transcendental functions
  31. Altmetric Badge
    Chapter 30 D’Alembert and Lagrange and the inequality technique
  32. Altmetric Badge
    Chapter 31 Fourier and Fourier series
  33. Altmetric Badge
    Chapter 32 Gauss and the hypergeometric series
  34. Altmetric Badge
    Chapter 33 Cauchy’s rejection of the 18th-century theory of series
Attention for Chapter 13: The young Euler between innovation and tradition
Altmetric Badge

Citations

dimensions_citation
3 Dimensions
You are seeing a free-to-access but limited selection of the activity Altmetric has collected about this research output. Click here to find out more.
Chapter title
The young Euler between innovation and tradition
Chapter number 13
Book title
The Rise and Development of the Theory of Series up to the Early 1820s
Published by
Springer, New York, NY, January 2008
DOI 10.1007/978-0-387-73468-2_13
Book ISBNs
978-0-387-73467-5, 978-0-387-73468-2
Authors

Giovanni Ferraro