Dienes P. The Taylor Series 1957

Textbook in PDF format

Classical treatise on the Taylor Series.
Professor Dienes has here performed a notable service to the mathematical world in assembling and ordering in a thoroughgoing manner the modern theories relating to the Taylor series.
Real Variables
Complex Algebra
Infinite Series
Elementary Functions
Complex Differentiation
Geometrical Language
Complex Integration
Biuniform Mapping. Picard's Theorem
Representation of Analytic Functions
Singularities of Analytic Functions
Overconvergence and Gap Theorems
Divergent Series
The Taylor Series on its Circle of Convergence
Divergence and Singularities
Bibliography
Index