See page 382 in [1], a paper I have found very enlightening.

[1] HARDY, G. H. (1905). A method for determining the behavior of certain classes of power series near a singular point on the circle of convergence. Proc. London Math. Soc. 2 381-389. https://ia800708.us.archive.org/view_archive.php?archive=/22/items/crossref-pre-1909-scholarly-works/10.1112%252Fplms%252Fs1-9.1.126.zip&file=10.1112%252Fplms%252Fs2-3.1.381.pdf

See page 382 in [1], a paper I have found very enlightening.

Reference

[1] HARDY, G. H. (1905), "A method for determining the behavior of certain classes of power series near a singular point on the circle of convergence", Proceedings of the London Mathematical Society 2, pp. 381-389, JFM 36.0474.01.