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

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

Table of Contents

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