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We consider analogues of the Miintz-Szasz theorem, as in Ll5j and [4j, for functions regular in an angle. This yields necessary and sufficient conditions for the existence of integral functions which are bounded in an angle and have gaps of a very regular nature in their power series expansion. In the case when the gaps are not so regular, similar results hold for formal power series which converge in the angle concerned.

Müntz-Szasz type approximation and the angular growth of lacunary integral functions