General properties of Taylor series 1896-1996 (Q1384990)

In this interesting survey article the author starts from a statement on Taylor series of Emile Borel in 1896: ``in general, the circle of convergence is a natural boundary.'' In the first part it is pointed out that ``in general'' meant ``almost surely'' giving several examples and interesting references of one hundred years of development. The second part deals with the concept of a universal Taylor series, where it is required that the partial sums are able to approximate the most as they can on compact sets situated in the exterior of the disc of convergence.