An Introduction to Theory of Infinite Series by T.J. I'A. Bromwich

Book Contents :-
1. Sequences and Limits 2. Series of Positive Terms 3. Series in General 4. Absolute Convergence 5. Double Series 6. Infinite Products 7. Series of Variable Terms 8. Power Series 9. Trigonometrical Formulae 10. Complex Series and Products 11. Special Complex Series and Functions 12. Non-Convergent Series Appendix I – Arithmetic Theory of Irrational Numbers and Limits Appendix II – Definitions of the Logarithmic and Exponential Functions Appendix III – Some Theorems on Functions: Infinite Integrals and the Gamma Function

About this book :-
"An Introduction to Theory of Infinite Series" by "T. J. I'A. Bromwich" is a foundational textbook on "infinite series" and their mathematical properties. It explains concepts of "convergence" and divergence with rigorous analysis, helping readers understand how infinite sums behave. The book develops ideas of "series theory" in a systematic way, making advanced mathematical principles accessible. The text contributes to "mathematical analysis" by exploring conditions under which series converge to finite values. It connects infinite processes with practical techniques used in modern mathematics and "calculus". Bromwich’s clear exposition supports the study of analytic methods and mathematical reasoning, offering valuable insights into infinite summation. For students and researchers of series and analysis, this work remains an important reference. It bridges classical mathematical thought with foundational ideas of modern analysis, supporting deeper understanding of infinite processes and convergence principles in mathematics.

Book Detail :-
Title: An Introduction to Theory of Infinite Series by T.J. I'A. Bromwich
Publisher: Macmillan and Co Ltd
Year: 1926
Pages: 558
Type: PDF
Language: English
ISBN-10 #: 160386122X
ISBN-13 #: 978-1603861229
License: Public Domain Work
Amazon: Amazon

About Author :-
The author Thomas John I'Anson Bromwich was a British mathematician known for his work in "infinite series" and "real analysis". He contributed to the study of convergence and rigorous mathematical methods, helping students understand analytical concepts with clarity. His writings emphasized "mathematical rigor" and systematic reasoning, influencing mathematical education and research. His book "An Introduction to Theory of Infinite Series" explores the properties of series and their convergence in detail. It became an important reference for studying "convergence", summability, and theoretical mathematics.

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