On Divergent Series
Abstract
The formula for infinite geometric series gives the sum of 1-1+-...=1/2, a result
any sane person would find absurd. Traditionally, such series have been
considered useless because they are divergent. After Newton and Leibniz
laid down the systematic foundations for infinite series and Cauchy
formalized our notions of convergence, various mathematicians started to
see the use of divergent series, particularly with respect to fourier series.
We will explore the historical development of the divergent series, and
several methods of summability that confirm the existence of sums for
divergent series.
Table of Contents
Complete List of References
- [FW1]
Ford, Walter Burton.
Studies on Divergent Series and Summability.
The Macmillan Co. 1916. New York, NY. pp. 75-101
- [HG1]
Hardy, G.H.
Divergent Series.
Oxford University Press. 1949. Oxford, UK. pp. 1-41, 64-147.
- [SS1]
Saxena, S.C. and Shah, S.M.
Introduction to Real Variable Theory.
International Textbook Co. 1972. Scranton, PA. pp. 217-227
