On zeros of partial sums of a mapping of the unit disk onto a sector

This paper gives a mapping of the unit disk onto a sector. There exist neighborhoods of the origin such that power series expansions of the mapping in terms of classical Gegenbauer polynomials, Mittag-Leffler polynomials, and hypergeometric functions were obtained. Each such expansion represents the mapping in a disk of appropriate radius. Also, the zero-free region of the partial sums of the mapping when the sectorial angle is maximum was studied.