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Summable Series and Convergence Factors
Charles N. Moore

Colloquium Publications
1938; 105 pp; softcover
Volume: 22
ISBN-10: 0-8218-4620-5
ISBN-13: 978-0-8218-4620-9
List Price: US$28
Member Price: US$22.40
Order Code: COLL/22
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Fairly early in the development of the theory of summability of divergent series, the concept of convergence factors was recognized as of fundamental importance in the subject. One of the pioneers in this field was C. N. Moore, the author of the book under review.... Moore classifies convergence factors into two types. In type I he places the factors which have only the property that they preserve convergence for a convergent series or produce convergence for a summable series. In type II he places the factors which not only maintain or produce convergence but have the additional property that they may be used to obtain the sum or generalized sum of the series. This book gives a generalized systematic treatment of the theory of convergence factors of both types, for simply infinite series and for multiple series, convergent and summable....

--Bulletin of the American Mathematical Society


Graduate students and research mathematicians interested in analysis.

Table of Contents

  • Introduction
  • Convergence factors in convergent series
  • Summation of series by Nörlund means
  • Convergence factors in summable series
  • Convergence factors in summable double series
  • Convergence factors in summable multiple series
  • Convergence factors in restrictedly convergent multiple series
  • Bibliography
  • Index
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