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

Reviews

"The book is especially good at counterexamples, and includes many of these to warn against pitfalls in reasoning and to show that all the hypotheses of the theorems are really needed. One especially nice feature is the use of Tannery's theorem, on interchanging limit and summation, throughout the book."

-- MAA Reviews

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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