On representation and series expansions of \(F(z)\) (Q1364765)

This paper is a sequel to previous works of \textit{D. S. Tselnik} [Complex Variables, Theory Appl. 25, No. 2, 159-171 (1994; Zbl 0827.30015); J. Math. Anal. Appl. 193, No. 2, 522-542 (1995; Zbl 0829.30016)]. Several results concerning the representation (by simpler functions) of an analytic function \(F(z)\) within a closed Jordan curve are provided, refining those obtained in the above mentioned papers. The following sections are included in this paper: representation of \(F(z)\) on a disk; behaviour of the Taylor series on the circle of convergence; partial fraction expansion of \(F(z)\); estimates for the remainders of Taylor series; four comments on Mittag-Leffler's theorem. The results are too technical to be reproduced here.