An Introduction to the Theory of Infinite Series (Classic Reprint)

Thomas John I'anson Bromwich

ISBN 10: 0260270563 / ISBN 13: 9780260270566

Published by Forgotten Books, 2018

About this Item

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Bibliographic Details

• Title: An Introduction to the Theory of Infinite Series (Classic Reprint)
• Publisher: Forgotten Books
• Publication Date: 2018
• Language: English
• ISBN 10: 0260270563
• ISBN 13: 9780260270566
• Binding: hardcover
• Condition: Good

About this title

Synopsis

Master the foundations of infinite series with clear, rigorous guidance.

This classic text introduces the logarithmic and exponential functions from first principles, building intuition through precise definitions, geometric insight, and step‑by‑step derivations. It then extends to the frontier of complex series, convergence, and related theorems, offering a coherent path from basic ideas to advanced techniques.

This edition presents a unified approach to key topics in infinite series, including the properties and applications of logarithms, the exponential function, and the behavior of complex sequences. Readers will see how limits, continuity, and monotonicity underpin convergence results, and how foundational theorems are used to analyze power series, rational approximations, and special functions. The text emphasizes logical development and practical calculation, with numerous examples and carefully explained arguments.

• Clear development of the logarithmic function, its definition, and fundamental properties.
• Transition to the exponential function and its role as the inverse of the logarithm.
• Introduction to complex sequences, convergence criteria, and the geometry of convergence regions.
• Guided exploration of power series, convergence radii, and classic convergence tests.

Ideal for students and self‑learners seeking a solid, historically grounded treatment of infinite series and their applications in analysis and beyond.