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An Introduction to the Theory of Infinite Series
T. J. l'a. Bromwich

AMS Chelsea Publishing
1926; 535 pp; hardcover
Volume: 335
ISBN-10: 0-8218-3976-4
ISBN-13: 978-0-8218-3976-8
List Price: US$65
Member Price: US$58.50
Order Code: CHEL/335.H
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This edition consists largely of a reproduction of the first edition (which was based on lectures on Elementary Analysis given at Queen's College, Galway, from 1902-1907), with additional theorems and examples. Additional material includes a discussion of the solution of linear differential equations of the second order; a discussion of elliptic function formulae; expanded treatment of asymptomatic series; a discussion of trigonometrical series, including Stokes's transformation and Gibbs's phenomenon; and an expanded Appendix II that includes an account of Napier's invention of logarithms.

Table of Contents

  • Sequences and limits
  • Series of positive terms
  • Series in general
  • Absolute convergence
  • Double series
  • Infinite products
  • Series of variable terms
  • Power series
  • Special power series
  • Trigonometrical formulae
  • Complex series and products
  • Special complex series and functions
  • Non-convergent series
  • Asymptotic series
  • Trigonometrical series
  • Appendix I. Arithmetic theory of irrational numbers and limits
  • Appendix II. Definitions of the logarithmic and exponential functions
  • Appendix III. Some theorems on infinite integrals and gamma-functions
  • Miscellaneous examples
  • Index of special integrals, products, and series
  • General index
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