ian I _ n for all n is known (3). This fact was obtained by showing it to be also true for the larger class of analytic functions called by W. Rogosinski (4) typically-real functions, that is, those functions f(z) which assume real values for, and only for, real values of z when z lies within the unit circle. However, for the class of odd typically-real functions the coefficients are not bounded, though they are bounded for odd univalent functions, a sub-class when the coefficients are real. The following example illustrates the unboundedness of the coefficients of an odd typically-real function: z)=Z+ z2 ___ + (1.2) (1 _ Z2)2 2 (1 _ Z2)2 (1 + z)21