Abstract
Rational representations are obtained for the functions in the unit disk, and the valences of these functions are computed. For p≥1, f 2p−2 and f 2p−1 are p-valent. The image of the unit disk under each of these functions is precisely determined. The Koebe function f 1(z)occurs naturally as a member of this sequence of functions, and it appears that the relationship of f 2p−1 to the classof functions p-valent on the unit disk generalizes, at least to some extent, the well-known relationship of the Koebe function to the class of univalent functions.
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