An Introduction To The Theory Of Infinite Series (1908)

An Introduction To The Theory Of Infinite Series is a book written by Thomas John Ianson Bromwich and published in 1908. The book is a comprehensive introduction to the theory of infinite series, covering topics such as convergence, divergence, and the summation of series. It also includes discussions on power series, Fourier series, and the Riemann zeta function. The book is written in a clear and concise manner, with numerous examples and exercises to help readers understand the concepts presented. It is aimed at undergraduate and graduate students in mathematics and physics, as well as researchers and professionals in these fields. Overall, An Introduction To The Theory Of Infinite Series is a valuable resource for anyone interested in the study of infinite series and their applications.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

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