Where did the examples of Abel's continuity theorem go?
Sergio A. Carrillo

TL;DR
This paper revisits Abel's continuity theorem for power series, exploring its historical context, applications, and reasons for its diminished presence in modern analysis education.
Contribution
It provides a comprehensive overview of Abel's theorem, highlighting its significance and encouraging renewed interest in its applications and historical development.
Findings
Historical analysis of Abel's theorem
Examples of applications in literature
Discussion on its educational decline
Abstract
Abel's continuity theorem for power series is a great tool to compute sums and prove properties of special functions. However, apart from two basic examples, this no longer occupies a place in Analysis courses. This note is an invitation to get acquainted with this theorem, its history, and many of its applications dispersed in the literature.
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Taxonomy
TopicsAnalytic Number Theory Research · Mathematical and Theoretical Analysis · Advanced Mathematical Identities
